This paper addresses the existence and uniqueness of strong solutions to stochastic porous media equations dX−ΔΨ(X) dt=B(X) dW(t) in bounded domains of ℝd with Dirichlet boundary conditions. Here Ψ is a maximal monotone graph in ℝ×ℝ (possibly multivalued) with the domain and range all of ℝ. Compared with the existing literature on stochastic porous media equations, no growth condition on Ψ is assumed and the diffusion coefficient Ψ might be multivalued and discontinuous. The latter case is encountered in stochastic models for self-organized criticality or phase transition.
Publié le : 2009-03-15
Classification:
Stochastic porous media equation,
Wiener process,
convex functions,
Itô’s formula,
76S05,
60H15
@article{1241099917,
author = {Barbu, Viorel and Da Prato, Giuseppe and R\"ockner, Michael},
title = {Existence of strong solutions for stochastic porous media equation under general monotonicity conditions},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 428-452},
language = {en},
url = {http://dml.mathdoc.fr/item/1241099917}
}
Barbu, Viorel; Da Prato, Giuseppe; Röckner, Michael. Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Ann. Probab., Tome 37 (2009) no. 1, pp. 428-452. http://gdmltest.u-ga.fr/item/1241099917/