Large time behaviour of the solutions to some nonlinear evolution equations

Alain Haraux

Commentationes Mathematicae Universitatis Carolinae (1985)

  • Volume: 026, Issue: 1, page 91-109
  • ISSN: 0010-2628

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Haraux, Alain. "Large time behaviour of the solutions to some nonlinear evolution equations." Commentationes Mathematicae Universitatis Carolinae 026.1 (1985): 91-109. <http://eudml.org/doc/17363>.

@article{Haraux1985,
author = {Haraux, Alain},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonlinear equations; heat equation; wave equation; hyperbolic systems; periodic and almost periodic solutions; global behaviour},
language = {eng},
number = {1},
pages = {91-109},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Large time behaviour of the solutions to some nonlinear evolution equations},
url = {http://eudml.org/doc/17363},
volume = {026},
year = {1985},
}

TY - JOUR
AU - Haraux, Alain
TI - Large time behaviour of the solutions to some nonlinear evolution equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1985
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 026
IS - 1
SP - 91
EP - 109
LA - eng
KW - nonlinear equations; heat equation; wave equation; hyperbolic systems; periodic and almost periodic solutions; global behaviour
UR - http://eudml.org/doc/17363
ER -

References

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  1. L. AMERIO G. PROUSE, Uniqueness and almost-periodicity theorems for a nonlinear wave equation, Atti Accad. Naz. Lincei Rend Cl. Sci. Pis. Mat. Natur 46 (1969), 1-8. (1969) MR0255993
  2. H. BREZIS, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam - London (1973). (1973) Zbl0252.47055MR0348562
  3. H. BREZIS, Problèmes unilatéraux, J. Math. Pures Appl. 51 (1972), 1-168. (1972) Zbl0237.35001MR0428137
  4. T. CAZENAVE A. HARAUX, Propriétés oscillatoires des solutions de certaines équations des ondes semi-linéaires, C.R.A.S. Paris, Ser. A, to appear (1984). (1984) MR0750743
  5. C. M. DAFERMOS M. SLEMROD, Asymptotic behavior of non linear contraction semi-groups, J. Funct. Analysis 12 (1973), 97-106. (1973) MR0346611
  6. C. M. DAFERMOS, Asymptotic behavior of Solutions of Evolution Equations, in Nonlinear Evolution Equations, M. G. Crandall editor, Academic Press (1978), 103-123. (1978) Zbl0499.35015MR0513814
  7. A. HARAUX, Comportement à l'infini pour une équation des ondes non linéaire dissipative, C.R.A.S. Paris, t. 287 Ser. A (1978), 507-509. (1978) MR0512092
  8. A. HARAUX, Nonlinear evolution equations: global behavior of solutions, Springer Lecture Notes in Math. 841 (1981). (1981) Zbl0461.35002MR0610796
  9. A. HARAUX, Almost periodic forcing for a wave equation with a nonlinear, local damping term, Proc. Roy Soc. Edinburgh, 94 A (1983), 195-212. (1983) Zbl0589.35076MR0709715
  10. A. HARAUX, On a uniqueness theorem of L. Amerio and G. Prouse, to appear in Proc. Roy. Soc. Edinburgh. Zbl0555.35090
  11. A. HARAUX, Stabilization of trajectories for some weakly damped hyperbolic equations, to appear. Zbl0535.35006
  12. A. HARAUX H. CABANNES, Almost periodic motion of a string vibrating against a straight, fixed obstacle, Nonlinear Analysis, T.M.A., 7 (2) (1983), 129-141. (1983) MR0688769
  13. A. HARAUX M. KIRANE, Estimations C 1 pour des problèmes paraboliques semi-linéairesm, Ann. Fac. Sci. Toulouse 5 (1983). (1983) MR0747194
  14. M. KIRANE G. TRONEL, Effet régularisant C ∞ dans les problèmes paraboliques, to appear. 
  15. M. SCHATZMAN, A hyperbolic problem of second order with unilateral constraints: the vibrating string with a concave obstacle, J. Math. Anal. Appl. 73 (1980), 138-191. (1980) Zbl0497.73059MR0560941
  16. G. F. WEBB, A reaction-diffusion system for a deterministic diffusive epidemic, J. Math. Anal, and Appl. 84 (1981), 150-161. (1981) MR0639529

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