Strong Solutions of Stochastic Generalized Porous Media Equations: Existence, Uniqueness and Ergodicity

2005/12/13 by Giuseppe Da Prato, Da Prato, Giuseppe, B. L. Rozovskiĭ +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60H15 #76S05 #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.math/0512259

openalex publication_date 2005/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Explicit conditions are presented for the existence, uniqueness and ergodicity of the strong solution to a class of generalized stochastic porous media equations. Our estimate of the convergence rate is sharp according to the known optimal decay for the solution of the classical (deterministic) porous medium equation.

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

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