Semilinear heat equations with distributions in Morrey spaces as initial data

Masao Yamazaki, Xiaofang Zhou

Research output: Contribution to journalArticle

1 Citation (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 Jan 1
Externally publishedYes

Fingerprint

Semilinear Heat Equation
Morrey Space
Stationary Solutions
Cauchy Problem
Global Solvability
Small Solutions
Norm

Keywords

  • Morrey spaces
  • Semigroup
  • Semilinear heat equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Semilinear heat equations with distributions in Morrey spaces as initial data. / Yamazaki, Masao; Zhou, Xiaofang.

In: Hokkaido Mathematical Journal, Vol. 30, No. 3, 01.01.2001, p. 537-571.

Research output: Contribution to journalArticle

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