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Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions

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  • Clini, Andrea

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.

Suggested Citation

  • Clini, Andrea, 2023. "Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 428-498.
    • Handle: RePEc:eee:spapps:v:159:y:2023:i:c:p:428-498
    DOI: 10.1016/j.spa.2023.02.007
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    References listed on IDEAS

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    1. Kurtz, Thomas G. & Xiong, Jie, 1999. "Particle representations for a class of nonlinear SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 103-126, September.
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