On the stochastic Burgers' equation in the real line

Annals of Probability

Volumn 27, Issue 2, 1999, Pages 782-802

  Gyöngy, István ^a   Nualart, David ^b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Space time white noise; Stochastic Burgers' equation

Indexed keywords

EID: 0039526862     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022677386     Document Type: Article

References (17)

1. BERTINI, L., CANCRINI, N. and JONA-LASINIO, G. (1994). The stochastic Burgers equation. Commun. Math. Phys. 165 211-232.
2. BURGERS, J. M. (1974). The Nonlinear Diffusion Equation. Reidel, Dordrecht.
3. CAIROLI, R. and WALSH, J. B. (1975). Stochastic integrals in the plane. Acta Math. 134 111-183.
4. CARDON-WEBER, C. (1998). Large deviations for a Burgers' type SPDE. Laboratoire de Probabilités Univ. Paris VI. Preprint N 447.
5. DA PRATO, G., DEBUSSCHE A. and TEMAM, R. (1994). Stochastic Burgers equation. In Nonlinear Differential Equations and Applications 389-402. Birkhäuser, Basel.
6. DA PRATO, G. and GATAREK, D. (1995). Stochastic Burgers equation. Stochastics Stochastics Rep. 52 29-41.
7. DA PRATO, G. and ZABCZYK, J. (1992). Stochastic equations in infinite equations. Encyclopedia of Mathematics and Its Applications. Cambridge Univ. Press.
8. FUNAKI, T. (1983). Random motion of strings and related evolution equations. Nagoya Math. J. 89 129-193.
9. GYÖNGY, I. (1988). Existence and uniqueness results for semilinear stochastic partial differential equations. Stochastic Process. Appl. 73 271-299.
10. GYÖNGY, I. (1995). On non-degenerate quasi-linear stochastic partial differential equations. Potential Analysis 4 157-171.
11. GYÖNGY, I. and ROVIRA, C. (1997). On stochastic partial differential equations with polynomial nonlinearities. Stochastics Stochastic Rep. To appear.
12. xx. Comm. Pure Appl. Math. 3 201-230.
13. LIONS, J.-L. (1969). Quelques Méthods de Resolution des Problémes aux Limites non Linéarie. Gauthier-Villars, Paris.
14. MANTHEY, R. (1988). On the Cauchy problem for reaction diffusion equations with noise. Math. Nachr. 136 209-228.
15. MANTHEY, R. and MITTMANN, K. (1997). The initial value problem for stochastic reaction diffusion equations with continuous reaction. Stochastic Anal. Appl. 15 555-583.
16. ROZOVSKII, B. L. (1990). Stochastic Evolution Systems. Kluwer, Dordrecht.
17. WALSH, J. B. (1986). An introduction to stochastic partial differential equations. École d'été de Probabilités de St. Flour XIV. Lecture Notes in Math. 1180 265-437. Springer, Berlin.