A Schauder-Tychonoff fixed-point approach for nonlinear L\'evy driven reaction-diffusion systems
Probability
2025-12-16 v2
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.
Cite
@article{arxiv.2312.00927,
title = {A Schauder-Tychonoff fixed-point approach for nonlinear L\'evy driven reaction-diffusion systems},
author = {Erika Hausenblas and Michael A. Högele and Fahim Kistosil},
journal= {arXiv preprint arXiv:2312.00927},
year = {2025}
}