On computational proofs of the existence of solutions to nonlinear parabolic problems

Mitsuhiro T. Nakao, Yoshitaka Watanabe

研究成果: Article査読

4 被引用数 (Scopus)

抄録

This paper is an extension of the preceding study (Nakao, this journal, 1991) in which we described a numerical verification method of the solution for one-space dimensional parabolic problems, to the several-space dimensional case. Here, numerical verification means the automatic proof of the existence of solutions to the problems by some numerical techniques on a computer. We reformulate the verification condition for nonlinear parabolic initial boundary value problems using the fixed-point problem of a compact operator on certain function spaces. As in the preceding study based upon a simple C0 finite-element approximation and its constructive a priori error estimates, a numerical verification procedure is presented with some numerical examples.

本文言語English
ページ(範囲)401-410
ページ数10
ジャーナルJournal of Computational and Applied Mathematics
50
1-3
DOI
出版ステータスPublished - 1994 5 20
外部発表はい

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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