The Stochastic Klausmeier System and A Stochastic Schauder-Tychonoff Type Theorem

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2023-10-13 DOI:10.1007/s11118-023-10107-3

Hausenblas, Erika, Tölle, Jonas M.

引用次数: 5

Abstract

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.

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随机Klausmeier系统和一个随机Schauder-Tychonoff型定理

一方面，研究了具有高斯乘性噪声的Klausmeier非线性平流扩散方程随机演化系统的非负鞅解的存在性和路径唯一性。另一方面，我们提出并验证了Schauder-Tychonoff不动点定理的一般随机版本，因为它的应用是证明随机Klausmeier系统解的存在性的必要步骤。系统的分析是基于变分技术和半群技术。我们还讨论了解的其他正则性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.