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- W4297435044 abstract "In this paper, we study the classical Keller - Segel system on a two-dimensional domain perturbed by a pair of Wiener processes, where the leading diffusion term is replaced by a porous media term. Since the randomness is intrinsic, the interpretation of the stochastic integral in the Stratonovich sense is natural. We construct a solution (integral) operator and establish its continuity and compactness properties in an appropriately chosen Banach space. In this manner, we formulate a stochastic version of the Schauder - Tychonoff Type Fixed Point Theorem which is specific to our problem to obtain a solution. In-kind, we achieve the existence of a martingale solution." @default.
- W4297435044 created "2022-09-28" @default.
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- W4297435044 date "2022-09-26" @default.
- W4297435044 modified "2023-09-24" @default.
- W4297435044 title "Martingale Solution to a Stochastic Chemotaxis System with Porous Medium Diffusion" @default.
- W4297435044 doi "https://doi.org/10.48550/arxiv.2209.12424" @default.
- W4297435044 hasPublicationYear "2022" @default.
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