On the large-time dynamics of a class of parabolic equations subjected to homogeneous white noise: Itô's case;Sur la dynamique asymptotique d'une classe d'équations paraboliques stochastiques modélisant la présence d'un bruit blanc homogène : Le cas d'Itô

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 326, Issue 11, 1998, Pages 1299-1304

  Chueshov, Igor D ^a   Vuillermot, Pierre A ^b  

^a V N KARAZIN KHARKIV NATIONAL UNIVERSITY   (Ukraine)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032090740     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(98)80183-3     Document Type: Article

References (21)

1. [1] Bernfeld S.R., Hu Y.Y., Vuillermot P.-A., Homogénéisation Spatiale et Équivalence Asymptotique pour une Classe d'Équations Paraboliques Semi-linéaires Non-Autonomes, C. R. Acad. Sci. Paris 320 Série I (1995) 859-862.
2. [2] Bernfeld S.R., Hu Y.Y., Vuillermot P.-A., Large-Time Asymptotic Equivalence for a Class of Non-Autonomous Semilinear Parabolic Equations, Bull. Sci. Math. (1998) (in press).
3. [3] Chueshov I.D., Vuillermot P.-A., On the Large-Time Dynamics of a Class of Random Parabolic Equations, C. R. Acad. Sci. Paris 322 Série I (1996) 1181-1186.
4. [4] Chueshov I.D., Vuillermot P.-A., Long-Time Behavior of Solutions to a Class of Quasilinear Parabolic Equations with Random Coefficients, Ann. Inst. Henri-Poincaré, Analyse non linéaire 15 (2) (1998) 191-232.
5. [5] Chueshov I.D., Vuillermot P.-A., On the Large-Time Dynamics of a Class of Parabolic Equations subjected to Homogeneous White Noise: Stratonovitch's Case, C. R. Acad. Sci. Paris 323 Série I (1996) 29-33.
6. [6] Chueshov I.D., Vuillermot P.-A., Long-Time Behavior of Solutions to a Class of Stochastic Parabolic Equations with Homogeneous White Noise: Stratonovitch's Case, Probab. Th. Rel. Fields (1998) (in press).
7. [7] Chueshov I.D., Vuillermot P.-A., Long-Time Behavior of Solutions to a Class of Stochastic Parabolic Equations with Homogeneous White Noise: Itô's Case, Manuscript, 1998.
8. [8] Chueshov I.D., Vuillermot P.-A., Monotone Methods for the Qualitative Analysis of Nonlinear Random and Stochastic Partial Differential Equations (Book in preparation).
9. [9] Friedman A., Partial Differential Equations, Krieger Publishing Co., 1976.
10. [10] Gihman I.I., Skorohod A.V., Stochastic Differential Equations, Berlin-Heidelberg New York, Springer-Verlag, 1972.
11. [11] Hess P., Periodic-Parabolic Boundary-Value Problems and Positivity, Pitman Res. Notes Math. 247, Harlaw, Longman Sci. Tech., 1991.
12. [12] Itô K., Mc H.P. Kean, Diffusion Processes and their Sample Paths, Berlin-Heidelberg-New York, Springer-Verlag, 1974.
13. [13] Krylov N.V., Rozovskii B.L., Stochastic Evolution Equations, J. Sov. Math. 16 (1981) 1233-1277.
14. [14] Neças J., Introduction to the Theory of Nonlinear Elliptic Equations, John Wiley and Sons, New York, 1986.
15. [15] Pardoux E., Équations aux Dérivées Partielles Stochastiques Non-linéaires Monotones : Étude de Solutions Fortes de Type Itô, Thèse, Université de Paris-Orsay, vol. 1556, 1975.
16. [16] Tuckwell H.C., The Effects of Random Selection on Gene Frequency. Math. Biosc. 30 (1976) 113-128.
17. [17] Turelli J.M., Random Environments and Stochastic Calculus, Theor. Popul. Biology 12 (1977) 140-178.
18. N, I. Global Stabilization Processes, J. Diff. Equations 94 (2) (1991) 228-253, II. Codimension-One Stable Manifolds, Differ. Integ. Eq. 5 (3) (1992) 693-720. III. Center Curves and Liapunov Stability, Nonlinear Analysis, TMA 22 (5) (1994) 533-559.
19. N, I. Global Stabilization Processes, J. Diff. Equations 94 (2) (1991) 228-253, II. Codimension-One Stable Manifolds, Differ. Integ. Eq. 5 (3) (1992) 693-720. III. Center Curves and Liapunov Stability, Nonlinear Analysis, TMA 22 (5) (1994) 533-559.
20. N, I. Global Stabilization Processes, J. Diff. Equations 94 (2) (1991) 228-253, II. Codimension-One Stable Manifolds, Differ. Integ. Eq. 5 (3) (1992) 693-720. III. Center Curves and Liapunov Stability, Nonlinear Analysis, TMA 22 (5) (1994) 533-559.
21. N, Proc. Amer. Math. Soc. 116 (3) (1992) 775-782.