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

Kazuhiro Ishige; Ryuichi Sato

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arXiv · 1404.6856

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

Kazuhiro Ishige·Ryuichi Sato

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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 $λψ$ as $λ\to 0$ or $λ\to\infty$ and the lower blow-up estimates of the solutions.

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Kazuhiro Ishige, Ryuichi Sato. 2014-04-28. Heat equation with a nonlinear boundary condition and uniformly local $L^r$ spaces. https://arxiv.org/abs/1404.6856

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