The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem

Fuente: arXiv
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Main Authors: Hausenblas, Erika, Tölle, Jonas M.
Format: Preprint
Published: 2019
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author Hausenblas, Erika
Tölle, Jonas M.
author_facet Hausenblas, Erika
Tölle, Jonas M.
contents On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative noise. On the other hand, we present and verify a general stochastic version of the Schauder-Tychonoff fixed point theorem, as its application is an essential step for showing existence of the solution to the stochastic Klausmeier system. The analysis of the system is based both on variational and semigroup techniques. We also discuss additional regularity properties of the solution.
format Preprint
id arxiv_https___arxiv_org_abs_1912_00996
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem
Hausenblas, Erika
Tölle, Jonas M.
Analysis of PDEs
Functional Analysis
Probability
Primary 35K57, 60H15, Secondary 37N25, 47H10, 76S05, 92C15
On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative noise. On the other hand, we present and verify a general stochastic version of the Schauder-Tychonoff fixed point theorem, as its application is an essential step for showing existence of the solution to the stochastic Klausmeier system. The analysis of the system is based both on variational and semigroup techniques. We also discuss additional regularity properties of the solution.
title The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem
topic Analysis of PDEs
Functional Analysis
Probability
Primary 35K57, 60H15, Secondary 37N25, 47H10, 76S05, 92C15
url https://arxiv.org/abs/1912.00996