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March 2009 Existence of strong solutions for stochastic porous media equation under general monotonicity conditions
Viorel Barbu, Giuseppe Da Prato, Michael Röckner
Ann. Probab. 37(2): 428-452 (March 2009). DOI: 10.1214/08-AOP408

Abstract

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.

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Viorel Barbu. Giuseppe Da Prato. Michael Röckner. "Existence of strong solutions for stochastic porous media equation under general monotonicity conditions." Ann. Probab. 37 (2) 428 - 452, March 2009. https://doi.org/10.1214/08-AOP408

Information

Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1162.76054
MathSciNet: MR2510012
Digital Object Identifier: 10.1214/08-AOP408

Subjects:
Primary: 60H15, 76S05

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 2 • March 2009
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