Solutions with time-dependent singular sets for the heat equation with absorption |
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Authors: | Jin Takahashi Hikaru Yamamoto |
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Institution: | 1. Department of Mathematical and Computing Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan;2. Department of Mathematics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan |
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Abstract: | We consider the heat equation with a superlinear absorption term in and study the existence of nonnegative solutions with an m-dimensional time-dependent singular set, where . We prove that if , then there are two types of singular solutions. Moreover, we show the uniqueness of the solutions and specify the exact behavior of the solutions near the singular set. |
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Keywords: | 35K58 35A20 35A01 Semilinear heat equation Singular solution Time-dependent singularity Higher dimensional singular set |
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