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.
@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://www.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://www.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://www.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://www.numdam.org/item/AIHPC_1998__15_2_191_0/

[1] R.A. Adams, "Sobolev Spaces", Academic Press, New York-London, 1975. | MR | Zbl

[2] D.G. Aronson and H.F. Weinberger, 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] S.R. Bernfeld, Y.Y. Hu and P. Vuillermot, 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] S.R. Bernfeld, Y.Y. Hu and P. Vuillermot, Large-Time Asymptotic Equivalence for a Class of Non-Autonomous Semilinear Parabolic Equations, Bull. Sci. Math., 1998 (in press). | MR | Zbl

[5] H. Brézis, Analyse Fonctionnelle : Théorie et Applications, Masson. Paris-New York, 1983. | MR | Zbl

[6] P. Brunowski, P. Polacik and B. Santsede, Convergence in General Periodic Parabolic Equations in One-Space Dimension, Nonlinear Analysis TMA. Vol. 18, No. 3. 1992. pp. 209-215. | MR | Zbl

[7] I.D. Chueshov and P. Vuillermot, 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] I.D. Chueshov and P. Vuillermot, 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] I.D. Chueshov and P. Vuillermot, Long-Time Behavior of Solutions to a Class of Stochastic Parabolic Equations with Homogeneous White Noise: Stratonovitch's Case, 1997 (preprint).

[10] I.P. Cornfeld, S.V. Fomin and Ya.G. Sinai, Ergodic Theory, Springer-Verlag, Berlin-Heidelberg-New York, 1982. | MR | Zbl

[11] E.N. Dancer and P. Hess, Stable Subharmonic Solutions in Periodic Reaction-Diffusion Equations, J. Differential Equations, Vol. 108, No 1, 1994, pp. 190-200. | MR | Zbl

[12] E.N. Dancer and P. Hess, Stability of Fixed Points for Order Preserving Discrete-Time Dynamical Systems, J. Reine Angew. Math., Vol. 419, 1991, pp. 125-139. | MR | Zbl

[13] D. Daners and P. Koch Medina, Abstract Evolution Equations, Periodic Problems and Applications, Pitman Research Notes in Mathematics Series, Langman Sci. Techn., Harlaw, Vol. 279, 1992. | MR | Zbl

[14] A. Figotin and L. Pastur, Spectra of Random and Almost-Periodic Schrödinger Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1992. | MR

[15] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Inc., Englewood Cliffs, N.J., 1964. | MR | Zbl

[16] P. Hess and H.F. Weinberger, 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] P. Hess, Periodic Parabolic Boundary-Value Problems and Positivity, Pitman Research Notes in Mathematics Series, Vol. 247, Langman Sci. Tech., Harlaw, 1990. | MR | Zbl

[18] T. Kato, Abstract Evolution Equations of Parabolic Type in Banach and Hilbert Spaces, Nagoya Math. Journal, Vol. 19, 1961, pp. 93-125. | MR | Zbl

[19] T. Kato Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1982. | MR | Zbl

[20] O.A. Ladyzenskaya, N.N. Uraltceva and V.A. Solonnikov, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. Transl. of Math. Monographs, Vol. 23, 1968.

[21] J. Neças, Introduction to the Theory of Nonlinear Elliptic Equations, John Wiley and Sons, New York, 1986. | MR | Zbl

[22] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin-Heidelberg-New York, 1983. | MR | Zbl

[23] B. Simon, Functional Integration and Quantum Physics, Academic Press, New York- London, 1979. | MR | Zbl

[24] P. Takac, 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] P. Vuillermot, 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] P. Vuillermot, 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] P. Vuillermot, 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] P. Vuillermot, 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