Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Attractors in inhomogeneous conservation laws and parabolic regularizations

Authors: Hai Tao Fan and Jack K. Hale
Journal: Trans. Amer. Math. Soc. 347 (1995), 1239-1254
MSC: Primary 35L65; Secondary 35B25, 58F39
MathSciNet review: 1270661
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The asymptotic behavior of inhomogeneous conservation laws is considered. The attractor of the equation is characterized. The relationship between attractors of the equation and that of its parabolic regularization is studied.

References [Enhancements On Off] (What's this?)

    V. Babin and M. I. Vishik (1989), Attractors of evolutionary equations, "Nauka", Moscow; English transl., North-Holland, Amsterdam, 1992. M. Dafermos (1977), Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J. 26, 1097-1119. Evans (1990), Weak convergence methods for nonlinear partial differential equations, CBMS Regional Conf. Ser. in Math., vol. 74, Amer. Math. Soc., Providence, RI. Fan and J. K. Hale (1992), Large time behavior in inhomogeneous conservation laws, Arch. Rat. Mech. Anal. (to appear). Fiedler and J. Mallet-Paret (1989), A Poincaré-Bendixson theorem for scalar reaction diffusion equations, Arch. Rational. Mech. Anal. 107, 325-345. F. Filippov (1960), Differential equations with discontinuous right hand side, Mat. Sb. (N.S.) 42, 99-128; English transl., Amer. Math. Soc. Transl. Ser. 2, Amer. Math. Soc., Providence, RI. K. Hale (1988), Asymptotic behavior of dissipative systems, Amer. Math. Soc., Providence, RI. N. Kruzkov (1970), First order quasilinear equations in several independent variables, Mat. Sb. (N.S.) 81, 228-255; English transl., Math. USSR-Sb. 10, 217-243. N. Lyberopoulos (1992), Large time structure of solutions of scalar conservation laws with a nonlinear source field, preprint. Murat (1978), Compacité par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5, 485-507. Tartar (1979), Compensated compactness and applications to partial differential equations, Heriot-Watt Sympos. in Vol. IV, Pitman, New York. Temam (1988), Infinite dimensional dynamical systems in mechanics and physics, Appl. Math. Sci., no. 68, Springer-Verlag, Berlin and New York. I. Vol’pert (1967), The space $BV$ and quasilinear equations, Mat. Sb. (N.S.) 73; English transl., Math. USSR-Sb. 2, 225-267.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35L65, 35B25, 58F39

Retrieve articles in all journals with MSC: 35L65, 35B25, 58F39

Additional Information

Keywords: Attractors, conservation laws, dynamical systems
Article copyright: © Copyright 1995 American Mathematical Society