Numerical verification for existence of a global-in-time solution to semilinear parabolic equations

Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shinichi Oishi

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper presents a method of numerical verification for the existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving the existence of a solution to the semilinear parabolic equations with the initial point t=t≥0. If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t∈(0,τ],τ>0 in a neighborhood of a numerical solution. Numerical results of obtaining a global-in-time solution for a certain semilinear parabolic equation are also given.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume315
DOIs
Publication statusPublished - 2017 May 1

Keywords

  • Global-in-time solution
  • Semilinear parabolic equations
  • Verified numerical computations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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