Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions

Andrea Clini

Stochastic Processes and their Applications, 2023, vol. 159, issue C, 428-498

Abstract: We establish pathwise existence of solutions for stochastic porous media and fast diffusion equations of type (1.1), in the full regime m∈(0,∞) and for any initial data u0∈L2(Q). Moreover, if the initial data is positive, solutions are pathwise unique. In turn, the solution map to (1.1) is a continuous function of the driving noise and it generates an associated random dynamical system. Finally, in the regime m∈{1}∪(2,∞), all the aforementioned results also hold for signed initial data.

Date: 2023
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DOI: 10.1016/j.spa.2023.02.007

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