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
Full-text PDF Free Access
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- Antonio Ambrosetti and Paul H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis 14 (1973), 349β381. MR 0370183, DOI https://doi.org/10.1016/0022-1236%2873%2990051-7
- Vieri Benci and Giovanna Cerami, Positive solutions of some nonlinear elliptic problems in exterior domains, Arch. Rational Mech. Anal. 99 (1987), no. 4, 283β300. MR 898712, DOI https://doi.org/10.1007/BF00282048
- H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983), no. 4, 313β345. MR 695535, DOI https://doi.org/10.1007/BF00250555
- H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983), no. 4, 313β345. MR 695535, DOI https://doi.org/10.1007/BF00250555
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- Eduard Feireisl, Convergence to an equilibrium for semilinear wave equations on unbounded intervals, Dynam. Systems Appl. 3 (1994), no. 3, 423β434. MR 1289815
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B. Gidas, W. Ni, and L. Nirenberg, Symmetry and related properties by the maximum principle, Comm. Math. Phys. 68, 209β243 (1979)
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J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, I., Dunod, Paris, 1968
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A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14, 349β381 (1973)
V. Benci and G. Cerami, Positive solutions of some nonlinear elliptic problems in exterior domains. Arch. Rational Mech. Anal. 99 (4), 283β300 (1987)
H. Berestycki and P. L. Lions, Nonlinear scalar field equations, I. Existence of a ground state, Arch. Rational Mech. Anal. 82, 313β346 (1983)
H. Berestycki and P. L. Lions, Nonlinear scalar field equations, II. Existence of infinitely many solutions, Arch. Rational Mech. Anal. 82, 347β376 (1983)
S. Coleman, V. Glazer, and A. Martin, Action minima among solutions to a class of Euclidean scalar field equations, Commun. Math. Phys. 58 (2), 211β221 (1978)
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, 1β14 (1982)
E. Feireisl, Convergence to an equilibrium for semilinear wave equations on unbounded intervals, Dynamic Syst. Appl. 3 (3), 423β434 (1994)
J. M. Ghidaglia and R. Temam, Attractors for damped nonlinear hyperbolic equations, J. Math. Pures Appl. 66, 273β319 (1987)
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, 485β511 (1987)
B. Gidas, W. Ni, and L. Nirenberg, Symmetry and related properties by the maximum principle, Comm. Math. Phys. 68, 209β243 (1979)
C. Keller, Stable and unstable manifolds for the nonlinear wave equation with dissipation, J. Differential Equations 50 (3), 330β347 (1983)
M. K. Kwong, Uniqueness of positive solutions of $\Delta u - u + {u^p} = 0$ in ${R^N}$, Arch. Rational Mech. Anal. 105, 243β266 (1989)
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, 1β21 (1974)
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
J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, I., Dunod, Paris, 1968
L. E. Payne and D. H. Sattinger, Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22, 273β303 (1975)
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
M. Remoissenet, Waves called solitons. Concepts and Experiments, Springer-Verlag, Berlin, Heidelberg, 1994
J. Shatah, Unstable ground state of nonlinear Klein-Gordon equations, Trans. Amer. Math. Soc. 290 (2), 701β711 (1985)
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© Copyright 1998
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