A Schauder-Tychonoff fixed-point approach for nonlinear Lévy driven reaction-diffusion systems

This article shows a stochastic version of the Schauder-Tychonoff fixed-point theoren and yields a stochastically weak solution to a large class of systems of nonlinear reaction-diffusion type equations driven by a cylindrical Wiener process and a Poisson random measure with certain moments. The mai...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Hausenblas, Erika, Högele, Michael A, Fahim Kistosil
Format: Article
Language:English
Subjects:
Coercivity
Nonlinear systems
Online Access:Get full text
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Summary:This article shows a stochastic version of the Schauder-Tychonoff fixed-point theoren and yields a stochastically weak solution to a large class of systems of nonlinear reaction-diffusion type equations driven by a cylindrical Wiener process and a Poisson random measure with certain moments. The main theorem solves systems whose reaction terms do not exhibit boundedness, dissipativity nor coercivity conditions.
ISSN:2331-8422