Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

Benjamin Fehrman; Benjamin Gess

Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

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arxiv 1712.05775 v3 pith:5WPRAAXH submitted 2017-12-15 math.AP math.PR

Benjamin Fehrman , Benjamin Gess This is my paper · ORCID

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keywords equationsnonlinearconservativediffusionnoisesouganidiswell-posednessanalogous

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We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends results of the second author and Souganidis, who considered analogous spatially homogeneous and first-order equations, and earlier works of Lions, Perthame, and Souganidis.

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Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing
math.AP 2019-08 reject novelty 6.0 of 10

Existence and uniqueness of invariant measures are claimed for anisotropic degenerate parabolic-hyperbolic conservation laws driven by additive white noise, extending Debussche-Vovelle's first-order theory.

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