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

Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)1185-1209
Number of pages25
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume37
Issue number5
DOIs
Publication statusPublished - 2020 Sep 1

Keywords

  • Higher-order semilinear parabolic equation
  • Majorizing kernel
  • Singular initial data
  • Solvability

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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