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.
| Original language | English |
|---|---|
| Pages (from-to) | 185-246 |
| Number of pages | 62 |
| Journal | Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis |
| Volume | 61.2024 |
| Issue number | August |
| DOIs | |
| Publication status | Published - 13 Oct 2023 |
Bibliographical note
Publisher Copyright: © The Author(s) 2023.Keywords
- Stochastic Klausmeier evolution system
- Stochastic Schauder-Tychonoff type theorem
- Pattern formation in ecology
- Nonlinear stochastic partial differential equation
- Flows in porous media, pathwise uniqueness
- 47H10
- 92C15
- 37N25
- 76S05
- 35K57
- 60H15