Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 15(2010) > Paper 17 open journal systems 


Support theorem for a stochastic Cahn-Hilliard equation

Lijun Bo, Department of Mathematics, Xidian University
Kehua Shi, School of Mathematical Sciences, Xiamen University
Yongjin Wang, School of Mathematical Sciences, Nankai University


Abstract
In this paper, we establish a Stroock-Varadhan support theorem for the global mild solution to a d (d ≤ 3)-dimensional stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise


Full text: PDF

Pages: 484-525

Published on: May 1, 2010
Bibliography
  1. Bally, Vlad; Millet, Annie; Sanz-Solé, Marta. Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations. Ann. Probab. 23 (1995), no. 1, 178--222. MR1330767 (96d:60091)
  2. Blowey, J. F.; Elliott, C. M. The Cahn-Hilliard gradient theory for phase separation with nonsmooth free energy. II. Numerical analysis. European J. Appl. Math. 3 (1992), no. 2, 147--179. MR1166255 (93g:80007)
  3. Bo, Lijun; Shi, Kehua; Wang, Yongjin. Jump type Cahn-Hilliard equations with fractional noises. Chin. Ann. Math. Ser. B 29 (2008), no. 6, 663--678. MR2470622 (2010c:35075)
  4. Bo, Lijun; Wang, Yongjin. Stochastic Cahn-Hilliard partial differential equations with Lévy spacetime white noises. Stoch. Dyn. 6 (2006), no. 2, 229--244. MR2239091 (2007i:60074)
  5. Cahn. J, Hilliard. J. Free energy for a nonuniform system I. Interfacial free energy. J. Chem. Phys. 2 (1958), 258--267.
  6. Cardon-Weber, Caroline. Cahn-Hilliard stochastic equation: existence of the solution and of its density. Bernoulli 7 (2001), no. 5, 777--816. MR1867082 (2002i:60109)
  7. Cardon-Weber, Caroline; Millet, Annie. A support theorem for a generalized Burgers SPDE. Potential Anal. 15 (2001), no. 4, 361--408. MR1856154 (2002g:60097)
  8. Da Prato, Giuseppe; Debussche, Arnaud. Stochastic Cahn-Hilliard equation. Nonlinear Anal. 26 (1996), no. 2, 241--263. MR1359472 (96k:35200)
  9. Da Prato, G.; Zabczyk, J. Ergodicity for infinite-dimensional systems.London Mathematical Society Lecture Note Series, 229. Cambridge University Press, Cambridge, 1996. xii+339 pp. ISBN: 0-521-57900-7 MR1417491 (97k:60165)
  10. Debussche, Arnaud; Dettori, Lucia. On the Cahn-Hilliard equation with a logarithmic free energy. Nonlinear Anal. 24 (1995), no. 10, 1491--1514. MR1327930 (96c:35080)
  11. Gyöngy, István. Existence and uniqueness results for semilinear stochastic partial differential equations. Stochastic Process. Appl. 73 (1998), no. 2, 271--299. MR1608641 (99b:60091)
  12. Gyöngy, István; Nualart, David. On the stochastic Burgers' equation in the real line. Ann. Probab. 27 (1999), no. 2, 782--802. MR1698967 (2000f:60091)
  13. Millet, Annie; Sanz-Solé, Marta. The support of the solution to a hyperbolic SPDE. Probab. Theory Related Fields 98 (1994), no. 3, 361--387. MR1262971 (95a:60089)
  14. Nakayama, Toshiyuki. Support theorem for mild solutions of SDE's in Hilbert spaces. J. Math. Sci. Univ. Tokyo 11 (2004), no. 3, 245--311. MR2097527 (2005k:60069)
  15. Novick-Cohen, Amy; Segel, Lee A. Nonlinear aspects of the Cahnmhy Hilliard equation. Phys. D 10 (1984), no. 3, 277--298. MR0763473 (85k:35120)
  16. Nualart, D.; Pardoux, É. White noise driven quasilinear SPDEs with reflection. Probab. Theory Related Fields 93 (1992), no. 1, 77--89. MR1172940 (93h:60093)
  17. Stroock, Daniel W.; Varadhan, S. R. S. On the support of diffusion processes with applications to the strong maximum principle. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, pp. 333--359. Univ. California Press, Berkeley, Calif., 1972. MR0400425 (53 #4259)
  18. Temam, Roger. Infinite-dimensional dynamical systems in mechanics and physics.Second edition.Applied Mathematical Sciences, 68. Springer-Verlag, New York, 1997. xxii+648 pp. ISBN: 0-387-94866-X MR1441312 (98b:58056)
  19. Walsh, John B. An introduction to stochastic partial differential equations. École d'été de probabilités de Saint-Flour, XIV---1984, 265--439, Lecture Notes in Math., 1180, Springer, Berlin, 1986. MR0876085 (88a:60114)













Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489