The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem
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In: Potential analysis, Vol. 61.2024, 13.10.2024, p. 185-246.
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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 -
