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

4 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

Fingerprint

Numerical Verification
Semilinear Parabolic Equation
Theorem
Sufficient Conditions
Numerical Solution
Numerical Results

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical verification for existence of a global-in-time solution to semilinear parabolic equations. / Mizuguchi, Makoto; Takayasu, Akitoshi; Kubo, Takayuki; Oishi, Shinichi.

In: Journal of Computational and Applied Mathematics, Vol. 315, 01.05.2017, p. 1-16.

Research output: Contribution to journalArticle

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