A Schauder-Tychonoff fixed-point approach for nonlinear L\'evy driven reaction-diffusion systems

Erika Hausenblas; Michael A. Högele; Fahim Kistosil

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arXiv · 2312.00927

A Schauder-Tychonoff fixed-point approach for nonlinear L\'evy driven reaction-diffusion systems

Erika Hausenblas·Michael A. Högele·Fahim Kistosil

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Abstract

We show a stochastic version of the Schauder-Tychonoff fixed point theorem which yields a solution of the martingale problem for a class of systems of nonlinear reaction-diffusion equations driven by a cylindrical Wiener process and a Poisson random measure with certain moments. By this type of theorem one can solve systems by linearization which have a possibly unbounded, non-dissipative and non-coercive nonlinearity.

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Erika Hausenblas, Michael A. Högele, Fahim Kistosil. 2023-12-01. A Schauder-Tychonoff fixed-point approach for nonlinear L\'evy driven reaction-diffusion systems. https://arxiv.org/abs/2312.00927

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