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Higher-dimensional moving singularities in a superlinear parabolic equation

Higher-dimensional moving singularities in a superlinear parabolic equation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Higher-dimensional moving singularities in a superlinear parabolic equation

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-018-0452-4
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Evolution Equations – Springer Journals

Published: May 29, 2018

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