A method of verified computations for solutions to semilinear parabolic equations using semigroup theory

Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, Shinichi Oishi

研究成果: Article

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This paper presents a numerical method for verifying the existence and local uniqueness of a solution for an initial-boundary value problem of semilinear parabolic equations. The main theorem of this paper provides a sufficient condition for a unique solution to be enclosed within a neighborhood of a numerical solution. In the formulation used in this paper, the initial-boundary value problem is transformed into a fixed-point form using an analytic semigroup. The sufficient condition is derived from Banach's fixed-point theorem. This paper also introduces a recursive scheme to extend a time interval in which the validity of the solution can be verified. As an application of this method, the existence of a global-in-time solution is demonstrated for a certain semilinear parabolic equation.

元の言語English
ページ(範囲)980-1001
ページ数22
ジャーナルSIAM Journal on Numerical Analysis
55
発行部数2
DOI
出版物ステータスPublished - 2017

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ASJC Scopus subject areas

  • Numerical Analysis

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