Existence and Uniqueness of Nonnegative Solutions to the Stochastic Porous Media Equation

2007/03/14 by Barbu, Viorel, Da Prato, Giuseppe, Röckner, Michael · 1 citation
#60H15 #76S05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.math/0703420

Abstract

One proves that the stochastic porous media equation in 3-D has a unique nonnegative solution for nonnegative initial data in H^-1(\mathcal O) if the nonlinearity is monotone and has polynomial growth.

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• Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases

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