\markboth{BIBLIOGRAPHY}BIBLIOGRAPHY

• G. Akagi and M. Otani, Evolution inclusions governed by subdifferentials in reflexive Banach spaces, Journal of Evolution Equations 4 (2004), 519–541.
• R. A. Adams, Sobolev spaces, Academic Press, New York (1975).
• M. Aida, M. A. Efendiev, and A. Yagi, Quasilinear abstract parabolic evolution equations and exponential attractor, Osaka Journal of Mathematics 42 (2005), 101–132.
• M. Aida, T. Tsujikawa, M. A. Efendiev, A. Yagi, and M. Mimura, Lower estimate of the attractor dimension for a chemotaxis growth system, Journal London Mathematical Society 74 (2006), 453–474.
• S. Agmon and L. Nirenberg, Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space, Communications on Pure and Applied Mathematics 20 (1967), 207–229.
• H. Amann and J. Escher, Analysis II, Grundstudium Mathematik, Birkhäuser, (1999).
• F. Andreu, J. Mazon, F. Simondon, and J. Toledo, Attractor for a degenerate nonlinear diffusion problem with nonlinear boundary condition, Journal of Dynamics and Differential Equations 10 (1998), no. 3, 347–377.
• G. Andrews and J. M. Ball, Asymptotic behavior and changes of phase in one-dimensional nonlinear viscoelasticity, Journal of Differential Equations 44 (1982), 306–341.
• A. Babin and M. I. Vishik, Attractors of Evolutionary Equations, Nauka, Moscow, 1989; English translation in Studies in Applied Mathematics 25, North-Holland, Amsterdam (1992).
• V. Belleri and V. Pata, Attractors for semilinear strongly damped wave equations on $\mathbb R^3$, Discrete and Continuous Dynamical Systems 7 (2001), no. 4, 719–735.
• A. Biryuk, Spectral properties of solutions of Burgers equation with small dissipation, Functional Analysis and Its Applications 35 (2001), 1–12.
• H. Brezis, Operateurs Maximaux Monotone et Semi-Groupes de Contractions dans les Espaces Hilbert, North-Holland Mathematics Studies 5 (1973).
• H. Brezis and M. Crandall, Uniqueness of solutions of the initial-value problem for $u_ {t}-\Delta \varphi (u)=0$, Journal de Mathématiques Pures et Appliquées 58(9) (1979), 2, 153–163.
• T. Caraballo, P. Kloeden, and J. Real, Pullback and forward attractors for a damped wave equation with delays, Stochastics and Dynamics 4 (2004), 405–423.
• A. N. Carvalho, J. A. Langa, J. C. Robinson, and A. Surez, Characterization of nonautonomous attractors of a perturbed infinite-dimensional gradient system, Journal of Differential Equations 236 (2007), 570–603.
• D. Cheban, P. Kloeden, and B. Schmalfuss, The relationship between pullback, forward and global attractors of nonautonomous dynamical systems, Nonlinear Dynamics and Systems Theory 2 (2002), 9–28.
• Y. Chen, Hölder estimates for solutions of uniformly degenerate quasilinear parabolic equations, Chinese Annals of Mathematics B 5 (4) (1984), 661–678.
• V. V. Chepyzhov and M. A. Efendiev, Hausdorff dimension estimation for attractors of nonautonomous dynamical systems in unbounded domains: An example, Communications on Pure and Applied Mathematics 53 (2000), 647–665.
• V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence, Rhode Island (2002).
• V. V. Chepyzhov and M. I. Vishik, Attractors of nonautonomous dynamical systems and their dimension, Journal de Mathématiques Pures et Appliquées 73 (1994), 279–333.
• V. V. Chepyzhov and M. I. Vishik, Kolmogorov’s $\varepsilon$-entropy for the attractor of reaction-diffusion equations, Sbornik: Mathematics 189 (2) (1998), 81–110.
• L. H. Chuan, T. Tsujikawa, and A. Yagi, Asymptotic behavior of solutions for forest kinematic model, Funkcialaj Ekvacioj 49 (3) (2006), 427–449.
• L. H. Chuan and A. Yagi, Dynamical system for forest kinematic model, Advances in Mathematical Sciences and Applications 16 (2006), 343–409.
• P. Colli, On some doubly nonlinear evolution equations in Banach spaces, Japan Journal of Industrial and Applied Mathematics 9 (2) (1992), 181–203.
• P. Colli and A. Visintin, On a class of doubly nonlinear evolution equations, Communications in Partial Differential Equations 15 (1990), no. 5, 737–756.
• J. W. Costerton, Z. Lewandowski, D. E. Caldwell, D. R. Korber, and H. M. Lappin-Scott, Microbial Biofilms, Annual Review Microbiology 49 (1995), 711–745.
• E. DiBenedetto, Degenerate Parabolic Equations (Universitext), Springer-Verlag, New York (1993).
• L. Dung and B. Nicolaenko, Exponential attractors in Banach spaces, Journal of Dynamics and Differential Equations 13 (2001), 791–806.
• A. Eden, C. Foias, B. Nicolaenko, and R. Temam, Exponential Attractors for Dissipative Evolution Equations, Research in Application Mathematics 37, John Wiley & Sons, New York (1994).
• A. Eden and J. Rakotoson, Exponential attractors for a doubly nonlinear equation, Journal of Mathematical Analysis and Applications 185 (2) (1994), 321–339.
• M. A. Efendiev, Evolution Equations Arising in the Modeling of Life Sciences, International Series of Numerical Mathematics, Vol. 163, Birkhäuser/Springer, 217 pages.
• M. A. Efendiev, Finite and Infinite Dimensional Attractors for Evolution Equations of Mathematical Physics, Gakkotoscho, Tokyo, 2010, 239 pages.
• M. A. Efendiev and L. Demaret, On the structure of attractors for a class of degenerate reaction-diffusion systems, Advances and Applications in Mathematical Sciences 18 (1) (2008), 105–118.
• M. A. Efendiev, R. Lasser, and S. Sonner, Necessary and sufficient conditions for an infinite system of parabolic equations preserving the positive cone, International Journal of Biomathematics and Biostatistics 1 (2010), 47–52.
• M. A. Efendiev, A. Miranville, and S. V. Zelik, Exponential attractors and finite-dimensional reduction for nonautonomous dynamical systems, Proceedings of the Royal Society of Edinburgh, Section A 135 (2005), 703–730.
• M. A. Efendiev, A. Miranville, and S. V. Zelik, Exponential attractors for a nonlinear reaction-diffusion system in $\mathbb {R}^3$, Comptes Rendus de l’Académie des Sciences, Series I, 330 (2000), 713–718.
• M. A. Efendiev, A. Miranville, and S. V. Zelik, Infinite dimensional attractors for a nonautonomous reaction-diffusion system, Mathematische Nachrichten 248–249 (2003), no. 1, 72–96.
• M. A. Efendiev and M. Otani, Attractors of some class degenerate-doubly nonlinear parabolic equations, Preprint IBB 41 (2007).
• M. A. Efendiev and M. Otani, Infinite dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium, Annales de l’Institut Henri Poincaré AN 28 (2011), 565–582.
• M. A. Efendiev and S. V. Zelik, Finite and infinite dimensional attractors for porous media equations, Proceedings London Mathematical Society 96 (2008), 51–77.
• M. A. Efendiev and S. Zelik, Finite dimensional attractors and exponential attractors for degenerate doubly nonlinear equations, Mathematical Methods in the Applied Sciences 32 (13) (2009), 1638–1668.
• M. A. Efendiev and S. V. Zelik, The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging, Advances in Differential Equations 8 (6) (2003), 673–732.
• M. A. Efendiev, S. V. Zelik, and H. J. Eberl, Existence and longtime behavior of a biofilm model, Communications on Pure and Applied Analysis 8 (2) (2009), 509–531.
• M. A. Efendiev and S. V. Zelik, Global attractor and stabilization for a coupled PDE-ODE system, Preprint IBB (2011).
• M. A. Efendiev and A. Yagi, Continuous dependence of exponential attractors for a parameter, Journal of the Mathematical Society of Japan 57 (2005), 167–181.
• P. Fabrie and A. Miranville, Exponential attractors for nonautonomous first-order evolution equations, Discrete and Continuous Dynamical Systems 4 (1998), 225–240.
• E. Feireisl, Ph. Laurencot, and F. Simondon, Global attractors for degenerate parabolic equations on unbounded domains, Journal of Differential Equations 129 (1996), no. 2, 239–261.
• R. M. Ford and R. W. Harvey, Role of chemotaxis in the transport of bacteria through saturated porous media, Advances in Water Resources 30 (2007), 1608–1617.
• H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin (1974).
• A. Y. Goritsky and M. I. Vishik, Integral manifolds for nonautonomous equations, Rendiconti Academia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni. 115 (21) (1997), 109–146.
• M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D 92 (1996), 178–192.
• R. Hagen, S. Roch, and B. Silbermann, C*-algebras and Numerical Analysis, CRC Press (2001).
• J. Hale, Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs 25, American Mathematical Society, Providence, Rhode Island (1988).
• A. Haraux, Systèmes Dynamiques Dissipatifs et Applications, Elsevier Masson (1991).
• D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer-Verlag, Berlin-New York (1981).
• D. Horstmann, From 1970 until Present: The Keller-Segel Model in chemotaxis and Its Consequences, Part I, Jahresbericht der Deutschen Mathematiker-Vereinigung 105(3) (2003), 103-165.
• A. V. Ivanov, Gradient estimates for doubly nonlinear parabolic equations, Journal of Mathematical Sciences 93 (5) (1999), 661-688.
• A. V. Ivanov, Second order quasilinear degenerate and nonuniformly elliptic and parabolic equations, Trudy Matematicheskogo Instituta imeni V. A. Steklova 160 (1982).
• S. Kamin and L. A. Peletier, Large time behavior of solutions of the porous media equation with absorption, Israel Journal of Mathematics 55 (2) (1986), 129-146.
• P. Kloeden, Pullback attractors of nonautonomous semidynamical systems, Stochastics and Dynamics 3 (2003), 101–112.
• A. N. Kolmogorov and V. M. Tikhomirov, $\varepsilon$-entropy and $\varepsilon$-capacity of sets in functional space, American Mathematical Society Translations 2, 17 (1961), 277–364.
• M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, MacMilian, New York (1964).
• P. Krejčí and S. Zheng, Pointwise asymptotic convergence of solutions for a phase separation model, Discrete and Continuous Dynamical Systems 16 (1) (2006), 1–18.
• N. Krylov, Nonlinear second order elliptic and parabolic equations, Moscow: Nauka (1985).
• Yu. Kuznetsov, M. Antonovsky, V. Biktashev, and A. Aponina, A cross-diffusion model of forest boundary dynamics, Journal of Mathematical Biology 32 (1994), 219–232.
• O. A. Ladyzhenskaya, Attractors for Semigroups and Evolution Equations, Lincei Lectures, Cambridge University Press (1991).
• O. A. Ladyzhenskaya, On the determination of minimal global attractors for Navier-Stokes equations and other partial differential equations, Uspekhi Matematicheskikh Nauk 42 (1987), 25–60.
• O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva, Linear and quasilinear equations of parabolic type, Nauka (1967).
• J. L. Lions, Quelques methodes de resolution des problemes aux limites non linearies, Dunod, Paris (1969).
• J. Malek and D. Prazak, Large time behavior by the method of $l$-trajectories, Journal of Differential Equations 181 (2002), 243–279.
• A. Mielke, Chapter 6: Evolution of Rate-independent Systems, C. Dafermos and E. Feireisl, eds., Handbook of Differential Equations, Evolutionary Equations, 2, 461–559.
• A. J. Milani and N. J. Koksch, An Introduction to Semiflows, Chapman & Hall/CRC, Boca Raton (2005).
• M. Mimura and T. Tsujikawa, Aggregating pattern dynamics in a chemotaxis model including growth, Journal Physica A 230 (1996), 499–543.
• T. Nagai, Blow-up of radially symmetric solutions to a chemotaxis system, Advances in Mathematical Sciences and Applications 5 (1995), 581–601.
• T. Nagai and T. Senba, Behavior of radially symmetric solutions of a system related to chemotaxis, Nonlinear Analysis 30 (1997), 3837–3842.
• T. Nagai and T. Senba, Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis, Advances in Mathematical Sciences and Applications 8 (1998), 145–156.
• H. Nakata, Numerical simulations for forest boundary dynamics model, Master Thesis, Osaka University (2004).
• S. M. Nikolskii, Approximation of Functions of Several Variables and Embedding Theorems (Russian), Nauka (1969).
• L. Nirenberg, Topic in Nonlinear Functional Analysis, Courant Institute Lecture Notes, New York University (1975).
• M. Otani, $L^\infty$-energy method and its applications, Nonlinear Partial Differential Equations and Their Applications 505-516, GAKUTO International Series, Mathematical Sciences and Applications, Gakkotosho, Tokyo 20 (2004).
• M. Otani, $L^\infty$-Energy Method, Basic tools and usage, Differential Equations, Chaos and Variational Problems: Progress in Nonlinear Differential Equations and Their Applications 75, Vasile Staicu (ed.), Birkhauser (2007), 357–376.
• M. Otani, Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators, Cauchy problems, Journal of Differential Equations 46 (12) (1982), 268-299.
• K. Osaki, T. Tsujikawa, A. Yagi, and M. Mimura, Exponential attractor for a chemotaxis-growth system of equations, Nonlinear Analysis 51 (2002), 119–144.
• R. Pego, Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and stability, Archive for Rational Mechanics and Analysis 97 (1987), 353–394.
• G. Raugel, Global Attractors in Partial Differential Equations, Handbook of Dynamical Systems 2, North-Holland (2002), 885–982.
• G. R. Sell and Y. You, Dynamics of Evolutionary Equations, Springer-Verlag, New York (2002).
• T. Senba, Blowup behavior of radial solutions to Jäger-Luckhaus system in high dimensional domains, Funkcialaj Ekvaciog (Fako de l’Funkcialaj Ekvacioj Japana Matematika Societo, Funkcialaj Ekvaciog, Serio Internacia) 48 (2) (2005), 247–271.
• T. Senba, Type II Blowup of Solutions to a Simplified Keller-Segel System in Two Dimensional Domains, Nonlinear Analysis Series A: Theory, Methods and Applications 66 (2007), 1817–1839.
• T. Senba and T. Suzuki, Chemotactic collapse in a parabolic-elliptic system of mathematical biology, Advances in Differential Equations 6 (1) (2001), 21–50.
• I. V. Skrypnik, Nonlinear Elliptic Boundary Value Problems, Teubner-Texte zur Mathematik 91, Leipzig (1986).
• A. Stevens and D. Horstmann, A constructive approach to traveling waves in chemotaxis, Journal of Nonlinear Science 14 (1) (2004), 1–25.
• Y. Sugiyama, Global existence in subcritical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel system, Differential and Integral Equations 20 (2006), 841–876.
• R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Springer-Verlag, New York (1988).
• H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam-New York (1978).
• A. Yagi, Abstract Parabolic Evolution Equations and Their Applications, Springer Monographs in Mathematics, Springer-Verlag, Berlin, Heidelberg (2010).
• J. L Vazquez, The porous medium equations, Clarendon Press, Oxford (2007).
• E. Zeidler, Nonlinear functional analysis and its applications, Springer-Verlag (1985).

\markboth{BIBLIOGRAPHY}BIBLIOGRAPHY

• G. Akagi and M. Otani, Evolution inclusions governed by subdifferentials in reflexive Banach spaces, Journal of Evolution Equations 4 (2004), 519–541.
• R. A. Adams, Sobolev spaces, Academic Press, New York (1975).
• M. Aida, M. A. Efendiev, and A. Yagi, Quasilinear abstract parabolic evolution equations and exponential attractor, Osaka Journal of Mathematics 42 (2005), 101–132.
• M. Aida, T. Tsujikawa, M. A. Efendiev, A. Yagi, and M. Mimura, Lower estimate of the attractor dimension for a chemotaxis growth system, Journal London Mathematical Society 74 (2006), 453–474.
• S. Agmon and L. Nirenberg, Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space, Communications on Pure and Applied Mathematics 20 (1967), 207–229.
• H. Amann and J. Escher, Analysis II, Grundstudium Mathematik, Birkhäuser, (1999).
• F. Andreu, J. Mazon, F. Simondon, and J. Toledo, Attractor for a degenerate nonlinear diffusion problem with nonlinear boundary condition, Journal of Dynamics and Differential Equations 10 (1998), no. 3, 347–377.
• G. Andrews and J. M. Ball, Asymptotic behavior and changes of phase in one-dimensional nonlinear viscoelasticity, Journal of Differential Equations 44 (1982), 306–341.
• A. Babin and M. I. Vishik, Attractors of Evolutionary Equations, Nauka, Moscow, 1989; English translation in Studies in Applied Mathematics 25, North-Holland, Amsterdam (1992).
• V. Belleri and V. Pata, Attractors for semilinear strongly damped wave equations on $\mathbb R^3$, Discrete and Continuous Dynamical Systems 7 (2001), no. 4, 719–735.
• A. Biryuk, Spectral properties of solutions of Burgers equation with small dissipation, Functional Analysis and Its Applications 35 (2001), 1–12.
• H. Brezis, Operateurs Maximaux Monotone et Semi-Groupes de Contractions dans les Espaces Hilbert, North-Holland Mathematics Studies 5 (1973).
• H. Brezis and M. Crandall, Uniqueness of solutions of the initial-value problem for $u_ {t}-\Delta \varphi (u)=0$, Journal de Mathématiques Pures et Appliquées 58(9) (1979), 2, 153–163.
• T. Caraballo, P. Kloeden, and J. Real, Pullback and forward attractors for a damped wave equation with delays, Stochastics and Dynamics 4 (2004), 405–423.
• A. N. Carvalho, J. A. Langa, J. C. Robinson, and A. Surez, Characterization of nonautonomous attractors of a perturbed infinite-dimensional gradient system, Journal of Differential Equations 236 (2007), 570–603.
• D. Cheban, P. Kloeden, and B. Schmalfuss, The relationship between pullback, forward and global attractors of nonautonomous dynamical systems, Nonlinear Dynamics and Systems Theory 2 (2002), 9–28.
• Y. Chen, Hölder estimates for solutions of uniformly degenerate quasilinear parabolic equations, Chinese Annals of Mathematics B 5 (4) (1984), 661–678.
• V. V. Chepyzhov and M. A. Efendiev, Hausdorff dimension estimation for attractors of nonautonomous dynamical systems in unbounded domains: An example, Communications on Pure and Applied Mathematics 53 (2000), 647–665.
• V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence, Rhode Island (2002).
• V. V. Chepyzhov and M. I. Vishik, Attractors of nonautonomous dynamical systems and their dimension, Journal de Mathématiques Pures et Appliquées 73 (1994), 279–333.
• V. V. Chepyzhov and M. I. Vishik, Kolmogorov’s $\varepsilon$-entropy for the attractor of reaction-diffusion equations, Sbornik: Mathematics 189 (2) (1998), 81–110.
• L. H. Chuan, T. Tsujikawa, and A. Yagi, Asymptotic behavior of solutions for forest kinematic model, Funkcialaj Ekvacioj 49 (3) (2006), 427–449.
• L. H. Chuan and A. Yagi, Dynamical system for forest kinematic model, Advances in Mathematical Sciences and Applications 16 (2006), 343–409.
• P. Colli, On some doubly nonlinear evolution equations in Banach spaces, Japan Journal of Industrial and Applied Mathematics 9 (2) (1992), 181–203.
• P. Colli and A. Visintin, On a class of doubly nonlinear evolution equations, Communications in Partial Differential Equations 15 (1990), no. 5, 737–756.
• J. W. Costerton, Z. Lewandowski, D. E. Caldwell, D. R. Korber, and H. M. Lappin-Scott, Microbial Biofilms, Annual Review Microbiology 49 (1995), 711–745.
• E. DiBenedetto, Degenerate Parabolic Equations (Universitext), Springer-Verlag, New York (1993).
• L. Dung and B. Nicolaenko, Exponential attractors in Banach spaces, Journal of Dynamics and Differential Equations 13 (2001), 791–806.
• A. Eden, C. Foias, B. Nicolaenko, and R. Temam, Exponential Attractors for Dissipative Evolution Equations, Research in Application Mathematics 37, John Wiley & Sons, New York (1994).
• A. Eden and J. Rakotoson, Exponential attractors for a doubly nonlinear equation, Journal of Mathematical Analysis and Applications 185 (2) (1994), 321–339.
• M. A. Efendiev, Evolution Equations Arising in the Modeling of Life Sciences, International Series of Numerical Mathematics, Vol. 163, Birkhäuser/Springer, 217 pages.
• M. A. Efendiev, Finite and Infinite Dimensional Attractors for Evolution Equations of Mathematical Physics, Gakkotoscho, Tokyo, 2010, 239 pages.
• M. A. Efendiev and L. Demaret, On the structure of attractors for a class of degenerate reaction-diffusion systems, Advances and Applications in Mathematical Sciences 18 (1) (2008), 105–118.
• M. A. Efendiev, R. Lasser, and S. Sonner, Necessary and sufficient conditions for an infinite system of parabolic equations preserving the positive cone, International Journal of Biomathematics and Biostatistics 1 (2010), 47–52.
• M. A. Efendiev, A. Miranville, and S. V. Zelik, Exponential attractors and finite-dimensional reduction for nonautonomous dynamical systems, Proceedings of the Royal Society of Edinburgh, Section A 135 (2005), 703–730.
• M. A. Efendiev, A. Miranville, and S. V. Zelik, Exponential attractors for a nonlinear reaction-diffusion system in $\mathbb {R}^3$, Comptes Rendus de l’Académie des Sciences, Series I, 330 (2000), 713–718.
• M. A. Efendiev, A. Miranville, and S. V. Zelik, Infinite dimensional attractors for a nonautonomous reaction-diffusion system, Mathematische Nachrichten 248–249 (2003), no. 1, 72–96.
• M. A. Efendiev and M. Otani, Attractors of some class degenerate-doubly nonlinear parabolic equations, Preprint IBB 41 (2007).
• M. A. Efendiev and M. Otani, Infinite dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium, Annales de l’Institut Henri Poincaré AN 28 (2011), 565–582.
• M. A. Efendiev and S. V. Zelik, Finite and infinite dimensional attractors for porous media equations, Proceedings London Mathematical Society 96 (2008), 51–77.
• M. A. Efendiev and S. Zelik, Finite dimensional attractors and exponential attractors for degenerate doubly nonlinear equations, Mathematical Methods in the Applied Sciences 32 (13) (2009), 1638–1668.
• M. A. Efendiev and S. V. Zelik, The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging, Advances in Differential Equations 8 (6) (2003), 673–732.
• M. A. Efendiev, S. V. Zelik, and H. J. Eberl, Existence and longtime behavior of a biofilm model, Communications on Pure and Applied Analysis 8 (2) (2009), 509–531.
• M. A. Efendiev and S. V. Zelik, Global attractor and stabilization for a coupled PDE-ODE system, Preprint IBB (2011).
• M. A. Efendiev and A. Yagi, Continuous dependence of exponential attractors for a parameter, Journal of the Mathematical Society of Japan 57 (2005), 167–181.
• P. Fabrie and A. Miranville, Exponential attractors for nonautonomous first-order evolution equations, Discrete and Continuous Dynamical Systems 4 (1998), 225–240.
• E. Feireisl, Ph. Laurencot, and F. Simondon, Global attractors for degenerate parabolic equations on unbounded domains, Journal of Differential Equations 129 (1996), no. 2, 239–261.
• R. M. Ford and R. W. Harvey, Role of chemotaxis in the transport of bacteria through saturated porous media, Advances in Water Resources 30 (2007), 1608–1617.
• H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin (1974).
• A. Y. Goritsky and M. I. Vishik, Integral manifolds for nonautonomous equations, Rendiconti Academia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni. 115 (21) (1997), 109–146.
• M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D 92 (1996), 178–192.
• R. Hagen, S. Roch, and B. Silbermann, C*-algebras and Numerical Analysis, CRC Press (2001).
• J. Hale, Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs 25, American Mathematical Society, Providence, Rhode Island (1988).
• A. Haraux, Systèmes Dynamiques Dissipatifs et Applications, Elsevier Masson (1991).
• D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer-Verlag, Berlin-New York (1981).
• D. Horstmann, From 1970 until Present: The Keller-Segel Model in chemotaxis and Its Consequences, Part I, Jahresbericht der Deutschen Mathematiker-Vereinigung 105(3) (2003), 103-165.
• A. V. Ivanov, Gradient estimates for doubly nonlinear parabolic equations, Journal of Mathematical Sciences 93 (5) (1999), 661-688.
• A. V. Ivanov, Second order quasilinear degenerate and nonuniformly elliptic and parabolic equations, Trudy Matematicheskogo Instituta imeni V. A. Steklova 160 (1982).
• S. Kamin and L. A. Peletier, Large time behavior of solutions of the porous media equation with absorption, Israel Journal of Mathematics 55 (2) (1986), 129-146.
• P. Kloeden, Pullback attractors of nonautonomous semidynamical systems, Stochastics and Dynamics 3 (2003), 101–112.
• A. N. Kolmogorov and V. M. Tikhomirov, $\varepsilon$-entropy and $\varepsilon$-capacity of sets in functional space, American Mathematical Society Translations 2, 17 (1961), 277–364.
• M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, MacMilian, New York (1964).
• P. Krejčí and S. Zheng, Pointwise asymptotic convergence of solutions for a phase separation model, Discrete and Continuous Dynamical Systems 16 (1) (2006), 1–18.
• N. Krylov, Nonlinear second order elliptic and parabolic equations, Moscow: Nauka (1985).
• Yu. Kuznetsov, M. Antonovsky, V. Biktashev, and A. Aponina, A cross-diffusion model of forest boundary dynamics, Journal of Mathematical Biology 32 (1994), 219–232.
• O. A. Ladyzhenskaya, Attractors for Semigroups and Evolution Equations, Lincei Lectures, Cambridge University Press (1991).
• O. A. Ladyzhenskaya, On the determination of minimal global attractors for Navier-Stokes equations and other partial differential equations, Uspekhi Matematicheskikh Nauk 42 (1987), 25–60.
• O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva, Linear and quasilinear equations of parabolic type, Nauka (1967).
• J. L. Lions, Quelques methodes de resolution des problemes aux limites non linearies, Dunod, Paris (1969).
• J. Malek and D. Prazak, Large time behavior by the method of $l$-trajectories, Journal of Differential Equations 181 (2002), 243–279.
• A. Mielke, Chapter 6: Evolution of Rate-independent Systems, C. Dafermos and E. Feireisl, eds., Handbook of Differential Equations, Evolutionary Equations, 2, 461–559.
• A. J. Milani and N. J. Koksch, An Introduction to Semiflows, Chapman & Hall/CRC, Boca Raton (2005).
• M. Mimura and T. Tsujikawa, Aggregating pattern dynamics in a chemotaxis model including growth, Journal Physica A 230 (1996), 499–543.
• T. Nagai, Blow-up of radially symmetric solutions to a chemotaxis system, Advances in Mathematical Sciences and Applications 5 (1995), 581–601.
• T. Nagai and T. Senba, Behavior of radially symmetric solutions of a system related to chemotaxis, Nonlinear Analysis 30 (1997), 3837–3842.
• T. Nagai and T. Senba, Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis, Advances in Mathematical Sciences and Applications 8 (1998), 145–156.
• H. Nakata, Numerical simulations for forest boundary dynamics model, Master Thesis, Osaka University (2004).
• S. M. Nikolskii, Approximation of Functions of Several Variables and Embedding Theorems (Russian), Nauka (1969).
• L. Nirenberg, Topic in Nonlinear Functional Analysis, Courant Institute Lecture Notes, New York University (1975).
• M. Otani, $L^\infty$-energy method and its applications, Nonlinear Partial Differential Equations and Their Applications 505-516, GAKUTO International Series, Mathematical Sciences and Applications, Gakkotosho, Tokyo 20 (2004).
• M. Otani, $L^\infty$-Energy Method, Basic tools and usage, Differential Equations, Chaos and Variational Problems: Progress in Nonlinear Differential Equations and Their Applications 75, Vasile Staicu (ed.), Birkhauser (2007), 357–376.
• M. Otani, Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators, Cauchy problems, Journal of Differential Equations 46 (12) (1982), 268-299.
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