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

Makoto Mizuguchi*, Akitoshi Takayasu, Takayuki Kubo, Shin'ichi Oishi

*この研究の対応する著者

研究成果: Article査読

10 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1-16
ページ数16
ジャーナルJournal of Computational and Applied Mathematics
315
DOI
出版ステータスPublished - 2017 5月 1

ASJC Scopus subject areas

  • 計算数学
  • 応用数学

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