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arXiv · 1909.05492

Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

Kazuhiro Ishige·Tatsuki Kawakami·Shinya Okabe
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Abstract

We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.

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Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe. 2019-09-12. Existence of solutions for a higher-order semilinear parabolic equation with singular initial data. https://arxiv.org/abs/1909.05492

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