Global well-posedness, dissipation and blow up for semilinear heat equations in energy spaces associated with self-adjoint operators

Masahiro Ikeda; Koichi Taniguchi

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arXiv · 1902.01016

Global well-posedness, dissipation and blow up for semilinear heat equations in energy spaces associated with self-adjoint operators

Masahiro Ikeda·Koichi Taniguchi

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Abstract

The purpose in this paper is to determine the global behavior of solutions to the initial-boundary value problems for energy-subcritical and critical semilinear heat equations by initial data with lower energy than the mountain pass level in energy spaces associated with self-adjoint operators satisfying Gaussian upper bounds. Our self-adjoint operators include the Dirichlet Laplacian on an open set, Robin Laplacian on an exterior domain, and Schr\"odinger operators, etc.

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Masahiro Ikeda, Koichi Taniguchi. 2019-02-04. Global well-posedness, dissipation and blow up for semilinear heat equations in energy spaces associated with self-adjoint operators. https://arxiv.org/abs/1902.01016

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