Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Finite energy travelling waves for nonlinear damped wave equations


Author: Eduard Feireisl
Journal: Quart. Appl. Math. 56 (1998), 55-70
MSC: Primary 35L70; Secondary 35A15, 35B40
DOI: https://doi.org/10.1090/qam/1604876
MathSciNet review: MR1604876
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  • [1] A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14, 349-381 (1973) MR 0370183
  • [2] V. Benci and G. Cerami, Positive solutions of some nonlinear elliptic problems in exterior domains. Arch. Rational Mech. Anal. 99 (4), 283-300 (1987) MR 898712
  • [3] H. Berestycki and P. L. Lions, Nonlinear scalar field equations, I. Existence of a ground state, Arch. Rational Mech. Anal. 82, 313-346 (1983) MR 695535
  • [4] H. Berestycki and P. L. Lions, Nonlinear scalar field equations, II. Existence of infinitely many solutions, Arch. Rational Mech. Anal. 82, 347-376 (1983) MR 695536
  • [5] S. Coleman, V. Glazer, and A. Martin, Action minima among solutions to a class of Euclidean scalar field equations, Commun. Math. Phys. 58 (2), 211-221 (1978) MR 0468913
  • [6] M. J. Esteban and P. L. Lions, Existence and non-existence results for semilinear elliptic problems in unbounded domains, Proc. Royal Soc. Edinburgh 93 A, 1-14 (1982) MR 688279
  • [7] E. Feireisl, Convergence to an equilibrium for semilinear wave equations on unbounded intervals, Dynamic Syst. Appl. 3 (3), 423-434 (1994) MR 1289815
  • [8] J. M. Ghidaglia and R. Temam, Attractors for damped nonlinear hyperbolic equations, J. Math. Pures Appl. 66, 273-319 (1987) MR 913856
  • [9] J. M. Ghidaglia and R. Temam, Regularity of the solutions of second order evolution equations and their attractors, Annali Scuola Normale Sup. Pisa Cl. Sci. 14, 485-511 (1987) MR 951230
  • [10] B. Gidas, W. Ni, and L. Nirenberg, Symmetry and related properties by the maximum principle, Comm. Math. Phys. 68, 209-243 (1979)
  • [11] C. Keller, Stable and unstable manifolds for the nonlinear wave equation with dissipation, J. Differential Equations 50 (3), 330-347 (1983) MR 723575
  • [12] M. K. Kwong, Uniqueness of positive solutions of $ \Delta u - u + {u^p} = 0$ in $ {R^N}$, Arch. Rational Mech. Anal. 105, 243-266 (1989) MR 969899
  • [13] H. A. Levine, Instability and nonexistence of global solutions of nonlinear wave equations of the form $ P{u_{tt}} = - Au + F\left( u \right)$, Trans. Amer. Math. Soc. 192, 1-21 (1974) MR 0344697
  • [14] P. L. Lions, On positive solutions of semilinear elliptic equations on unbounded domains, in Nonlinear Diffusion Equations and Their Equilibrium States, II, W. M. Ni, L. A. Peletier, J. Serrin, Editors, Math. Sci. Res. Inst. Publ. 13, Springer-Verlag, New York, Heidelberg, Berlin, 1988 MR 956083
  • [15] J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, I., Dunod, Paris, 1968
  • [16] L. E. Payne and D. H. Sattinger, Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22, 273-303 (1975) MR 0402291
  • [17] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Appl. Math. Sci., vol. 44, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983 MR 710486
  • [18] M. Remoissenet, Waves called solitons. Concepts and Experiments, Springer-Verlag, Berlin, Heidelberg, 1994 MR 1299532
  • [19] J. Shatah, Unstable ground state of nonlinear Klein-Gordon equations, Trans. Amer. Math. Soc. 290 (2), 701-711 (1985) MR 792821

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DOI: https://doi.org/10.1090/qam/1604876
Article copyright: © Copyright 1998 American Mathematical Society

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