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A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory
http://hdl.handle.net/2241/00146623
http://hdl.handle.net/2241/001466235178c859-ab38-4e79-8740-fcc5dec8501e
名前 / ファイル | ライセンス | アクション |
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SIAM_JNA_55-2 (451.4 kB)
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Item type | Journal Article(1) | |||||
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公開日 | 2017-06-27 | |||||
タイトル | ||||||
タイトル | A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
Mizuguchi, Makoto
× Mizuguchi, Makoto× Takayasu, Akitoshi× Kubo, Takayuki× Oishi, Shin'ichi |
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著者別名 |
高安, 亮紀
× 高安, 亮紀× 久保, 隆徹 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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. | |||||
書誌情報 |
SIAM journal on numerical analysis 巻 55, 号 2, p. 980-1001, 発行日 2017-04 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0036-1429 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA00831298 | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1137/141001664 | |||||
権利 | ||||||
権利情報 | © 2017, Society for Industrial and Applied Mathematics | |||||
著者版フラグ | ||||||
値 | publisher | |||||
出版者 | ||||||
出版者 | SIAM journal on numerical analysis |