@article{AIHPC_1998__15_2_191_0,
author = {Chueshov, Igor D. and Vuillermot, Pierre-A.},
title = {Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {191--232},
publisher = {Gauthier-Villars},
volume = {15},
number = {2},
year = {1998},
mrnumber = {1614575},
zbl = {0930.60046},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1998__15_2_191_0/}
}
TY - JOUR AU - Chueshov, Igor D. AU - Vuillermot, Pierre-A. TI - Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients JO - Annales de l'I.H.P. Analyse non linéaire PY - 1998 SP - 191 EP - 232 VL - 15 IS - 2 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPC_1998__15_2_191_0/ LA - en ID - AIHPC_1998__15_2_191_0 ER -
%0 Journal Article %A Chueshov, Igor D. %A Vuillermot, Pierre-A. %T Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients %J Annales de l'I.H.P. Analyse non linéaire %D 1998 %P 191-232 %V 15 %N 2 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPC_1998__15_2_191_0/ %G en %F AIHPC_1998__15_2_191_0
Chueshov, Igor D.; Vuillermot, Pierre-A. Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) no. 2, pp. 191-232. http://archive.numdam.org/item/AIHPC_1998__15_2_191_0/
[1] , "Sobolev Spaces", Academic Press, New York-London, 1975. | MR | Zbl
[2] and , Nonlinear Dynamics in Population Genetics, Combustion and Nerve Pulse Propagation. In Partial Differential Equations and Related Topics, J. A. Goldstein, Ed., pp. 5-49, Lecture Notes in Mathematics, Vol. 446, Springer-Verlag, Berlin-Heidelberg-New York, 1975. | MR | Zbl
[3] , and , Homogénéisation Spatiale et Équivalence Asymptotique pour une Classe d'Équations Paraboliques Semilinéaires Non Autonomes, C. R. Acad. Sci. Paris, Vol. 320, Série I, 1995, pp. 859-862. | MR | Zbl
[4] , and , Large-Time Asymptotic Equivalence for a Class of Non-Autonomous Semilinear Parabolic Equations, Bull. Sci. Math., 1998 (in press). | MR | Zbl
[5] , Analyse Fonctionnelle : Théorie et Applications, Masson. Paris-New York, 1983. | MR | Zbl
[6] , and , Convergence in General Periodic Parabolic Equations in One-Space Dimension, Nonlinear Analysis TMA. Vol. 18, No. 3. 1992. pp. 209-215. | MR | Zbl
[7] and , On the Large-Time Dynamics of a Class of Random Parabolic Equations, C. R. Acad. Sci. Paris, Vol. 322, Série I, 1996, pp. 1181-1186. | MR | Zbl
[8] and , On the Large-Time Dynamics of a Class of Parabolic Equations Subjected to Homogeneous White Noise: Stratonovitch's Case, C. R. Acad. Sci. Paris, Vol. 323, Série I, 1996, pp. 29-33. | MR | Zbl
[9] and , Long-Time Behavior of Solutions to a Class of Stochastic Parabolic Equations with Homogeneous White Noise: Stratonovitch's Case, 1997 (preprint).
[10] , and , Ergodic Theory, Springer-Verlag, Berlin-Heidelberg-New York, 1982. | MR | Zbl
[11] and , Stable Subharmonic Solutions in Periodic Reaction-Diffusion Equations, J. Differential Equations, Vol. 108, No 1, 1994, pp. 190-200. | MR | Zbl
[12] and , Stability of Fixed Points for Order Preserving Discrete-Time Dynamical Systems, J. Reine Angew. Math., Vol. 419, 1991, pp. 125-139. | MR | Zbl
[13] and , Abstract Evolution Equations, Periodic Problems and Applications, Pitman Research Notes in Mathematics Series, Langman Sci. Techn., Harlaw, Vol. 279, 1992. | MR | Zbl
[14] and , Spectra of Random and Almost-Periodic Schrödinger Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1992. | MR
[15] , Partial Differential Equations of Parabolic Type, Prentice Hall, Inc., Englewood Cliffs, N.J., 1964. | MR | Zbl
[16] and , Convergence to Spatial-Temporal Clines in the Fisher Equations with Time-Periodic Fitnesses, J. Math. Biol., Vol. 28, No. 1, 1990, pp. 83-98. | MR | Zbl
[17] , Periodic Parabolic Boundary-Value Problems and Positivity, Pitman Research Notes in Mathematics Series, Vol. 247, Langman Sci. Tech., Harlaw, 1990. | MR | Zbl
[18] , Abstract Evolution Equations of Parabolic Type in Banach and Hilbert Spaces, Nagoya Math. Journal, Vol. 19, 1961, pp. 93-125. | MR | Zbl
[19] Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1982. | MR | Zbl
[20] , and , Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. Transl. of Math. Monographs, Vol. 23, 1968.
[21] , Introduction to the Theory of Nonlinear Elliptic Equations, John Wiley and Sons, New York, 1986. | MR | Zbl
[22] , Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin-Heidelberg-New York, 1983. | MR | Zbl
[23] , Functional Integration and Quantum Physics, Academic Press, New York- London, 1979. | MR | Zbl
[24] , Linearly Stable Subharmonics in Strongly Monotone Time-Periodic Dynamical Systems, Proc. Am. Math. Soc., Vol. 115, No. 3, 1992, pp. 691-698. | MR | Zbl
[25] , Almost-Periodic Attractors for a Class of Non-Autonomous Reaction-Diffusion Equations on RN, I. Global Stabilization Processes, J. Differential Equations, Vol. 94, No. 2, 1991, pp. 228-253. | MR | Zbl
[26] , Almost-Periodic Attractors for a Class of Non-Autonomous Reaction-Diffusion Equations on RN, II. Codimension-One Stable Manifolds, Differential and Integral Equations, Vol. 5, No. 3, 1992, pp. 693-720. | MR | Zbl
[27] , Global Exponential Attractors for a Class of Almost-Periodic Parabolic Equations on RN, Proc. Am. Math. Soc., Vol. 116, No. 3, 1992, pp. 775-782. | MR | Zbl
[28] , Almost-Periodic Attractors for a Class of Non-Autonomous Reaction-Diffusion Equations on RN, III. Center Curves and Liapounov Stability, Nonlinear Analysis TMA, Vol. 22. No. 5. 1994, pp. 533-559. | MR | Zbl
