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

2 引用 (Scopus)

抄録

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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Semigroup Theory
Semilinear Parabolic Equation
Initial-boundary-value Problem
Boundary value problems
Banach Fixed Point Theorem
Analytic Semigroup
Sufficient Conditions
Unique Solution
Numerical methods
Uniqueness
Fixed point
Numerical Methods
Numerical Solution
Interval
Formulation
Theorem
Form

ASJC Scopus subject areas

  • Numerical Analysis

これを引用

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AU - Oishi, Shinichi

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