Heat equation with a nonlinear boundary condition and uniformly local Lr spaces

Kazuhiro Ishige; Ryuichi Sato

doi:10.3934/dcds.2016.36.2627

Heat equation with a nonlinear boundary condition and uniformly local L^r spaces

Kazuhiro Ishige, Ryuichi Sato

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local Lr spaces. Furthermore, we study the sharp lower estimates of the blow-up time of the solutions with the initial data λψ as λ → 0 or λ → ∞ and the lower blow-up estimates of the solutions.

Original language	English
Pages (from-to)	2627-2652
Number of pages	26
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	36
Issue number	5
DOIs	https://doi.org/10.3934/dcds.2016.36.2627
Publication status	Published - 2016 May

Keywords

Blow-up rate
Blow-up time
Heat equation
Nonlinear boundary condition
Uniformly local L spaces

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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