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Higher-dimensional moving singularities in a superlinear parabolic equation

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Abstract

This paper is concerned with the existence of singular solutions of a superlinear parabolic equation. It is shown that under some growth conditions on the nonlinearity, there exists a solution whose singularity forms a one or higher-dimensional time-dependent set. Such solutions are constructed by modifying singular solutions of the linear heat equation.

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Authors and Affiliations

  1. Department of Mathematics, Mandalay University, Mandalay, Myanmar

    Khin Phyu Phyu Htoo

  2. Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo, 152-8551, Japan

    Jin Takahashi

  3. Department of Mathematics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan

    Eiji Yanagida

Authors
  1. Khin Phyu Phyu Htoo
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  2. Jin Takahashi
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  3. Eiji Yanagida
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Corresponding author

Correspondence to Eiji Yanagida.

Additional information

Jin Takahashi was supported by JSPS KAKENHI Grant-in-Aid for JSPS Fellows (No. 17J00693). Eiji Yanagida was supported by JSPS KAKENHI Grant-in-Aid for Challenging Exploratory Research (No. 16K13769).

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Htoo, K.P.P., Takahashi, J. & Yanagida, E. Higher-dimensional moving singularities in a superlinear parabolic equation. J. Evol. Equ. 18, 1575–1593 (2018). https://doi.org/10.1007/s00028-018-0452-4

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  • DOI: https://doi.org/10.1007/s00028-018-0452-4

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