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

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The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem. / Hausenblas, Erika; Tölle, Jonas M.
in: Potential analysis, Jahrgang 61.2024, 13.10.2024, S. 185-246.

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

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Hausenblas E, Tölle JM. The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem. Potential analysis. 2024 Okt 13;61.2024:185-246. doi: 10.1007/s11118-023-10107-3

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@article{a8185853634c4ea2853135b176e14950,
title = "The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem",
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.",
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",
author = "Erika Hausenblas and T{\"o}lle, {Jonas M.}",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2023.",
year = "2024",
month = oct,
day = "13",
doi = "10.1007/s11118-023-10107-3",
language = "English",
volume = "61.2024",
pages = "185--246",
journal = "Potential analysis",
issn = "0926-2601",
publisher = "Kluwer Academic Publishers",

}

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TY - JOUR

T1 - The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem

AU - Hausenblas, Erika

AU - Tölle, Jonas M.

N1 - Publisher Copyright: © The Author(s) 2023.

PY - 2024/10/13

Y1 - 2024/10/13

N2 - 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.

AB - 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.

KW - Stochastic Klausmeier evolution system

KW - Stochastic Schauder-Tychonoff type theorem

KW - Pattern formation in ecology

KW - Nonlinear stochastic partial differential equation

KW - Flows in porous media, pathwise uniqueness

KW - 47H10

KW - 92C15

KW - 37N25

KW - 76S05

KW - 35K57

KW - 60H15

UR - http://www.scopus.com/inward/record.url?scp=85174181687&partnerID=8YFLogxK

U2 - 10.1007/s11118-023-10107-3

DO - 10.1007/s11118-023-10107-3

M3 - Article

VL - 61.2024

SP - 185

EP - 246

JO - Potential analysis

JF - Potential analysis

SN - 0926-2601

ER -