Semilinear heat equations with distributions in Morrey spaces as initial data

Masao Yamazaki*, Xiaofang Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

This paper is a continuous study to the paper [27]. Here we consider in Morrey spaces the Cauchy problem of the general semilinear heat equation with an external force. Both the external force and initial data belong to suitable Morrey spaces. When the norm of the external force is small, we proved the unique existence of small solution to the corresponding stationary problem. Moreover, if the initial data is close enough to the stationary solution, we verified the time-global solvability of the Cauchy problem, which leads to the stability of the small stationary solution.

Original languageEnglish
Pages (from-to)537-571
Number of pages35
JournalHokkaido Mathematical Journal
Volume30
Issue number3
DOIs
Publication statusPublished - 2001
Externally publishedYes

Keywords

  • Morrey spaces
  • Semigroup
  • Semilinear heat equations

ASJC Scopus subject areas

  • Mathematics(all)

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