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arXiv · 1804.00985

Note for global existence of semilinear heat equation in weighted $L^\infty$

Kazumasa Fujiwara·Vladimir Georgiev·Tohru Ozawa
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Abstract

The local and global existence of the Cauchy problem for semilinear heat equations with small data is studied in the weighted $L^\infty (\mathbb R^n)$ framework by a simple contraction argument. The contraction argument is based on a weighted uniform control of solutions related with the free solutions and the first iterations for the initial data of negative power.

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Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa. 2018-04-25. Note for global existence of semilinear heat equation in weighted $L^\infty$. https://arxiv.org/abs/1804.00985

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