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

Mitsuhiro T. Nakao, Yoshitaka Watanabe

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)401-410
    Number of pages10
    JournalJournal of Computational and Applied Mathematics
    Volume50
    Issue number1-3
    DOIs
    Publication statusPublished - May 20 1994

    All Science Journal Classification (ASJC) codes

    • Computational Mathematics
    • Applied Mathematics

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