Well-Posedness of Initial-Boundary Value Problems for a Reaction-Diffusion Equation

Autor:	Himonas, A. Alexandrou, Mantzavinos, Dionyssios, Yan, Fangchi
Rok vydání:	2018
Předmět:	Mathematics - Analysis of PDEs 35K57 35K20 35K05
Druh dokumentu:	Working Paper
Popis:	A reaction-diffusion equation with power nonlinearity formulated either on the half-line or on the finite interval with nonzero boundary conditions is shown to be locally well-posed in the sense of Hadamard for data in Sobolev spaces. The result is established via a contraction mapping argument, taking advantage of a novel approach that utilizes the formula produced by the unified transform method of Fokas for the forced linear heat equation to obtain linear estimates analogous to those previously derived for the nonlinear Schr\"odinger, Korteweg-de Vries and "good" Boussinesq equations. Thus, the present work extends the recently introduced "unified transform method approach to well-posedness" from dispersive equations to diffusive ones. Comment: 33 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.05322 Zobrazit plný text záznamu View this record from Arxiv