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

Kazuhiro Ishige; Ryuichi Sato

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

Analysis of PDEs 2014-04-29 v1

Authors: Kazuhiro Ishige , Ryuichi Sato

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 $L^r$ spaces. Furthermore, we study the sharp lower estimates of the blow-up time of the solutions with the initial data $\lambda\psi$ as $\lambda\to 0$ or $\lambda\to\infty$ and the lower blow-up estimates of the solutions.

Keywords

heat equation nonlinear boundary condition uniformly local L^r spaces local existence uniqueness blow-up time lower estimates

Cite

@article{arxiv.1404.6856,
  title  = {Heat equation with a nonlinear boundary condition and uniformly local $L^r$ spaces},
  author = {Kazuhiro Ishige and Ryuichi Sato},
  journal= {arXiv preprint arXiv:1404.6856},
  year   = {2014}
}

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