The Robin problems for the coupled system of reaction–diffusion equations

Autor:	Po-Chun Huang, Bo-Yu Pan
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Coupled system of reaction Diffusion equations Unified transform method The local well-posedness of the coupled system of reaction Analysis QA299.6-433
Zdroj:	Boundary Value Problems, Vol 2024, Iss 1, Pp 1-37 (2024)
Druh dokumentu:	article
ISSN:	1687-2770
DOI:	10.1186/s13661-024-01835-5
Popis:	Abstract This article investigates the local well-posedness of Turing-type reaction–diffusion equations with Robin boundary conditions in the Sobolev space. Utilizing the Hadamard norm, we derive estimates for Fokas unified transform solutions for linear initial-boundary value problems subject to external forces. Subsequently, we demonstrate that the iteration map, defined by the unified transform solutions and incorporating nonlinearity instead of external forces, acts as a contraction map within an appropriate solution space. Our conclusive result is established through the application of the contraction mapping theorem.
Databáze:	Directory of Open Access Journals
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