Generalized quasi-reversibility method for a backward heat equation with a fractional Laplacian

Hajime Koba, Hideki Matsuoka

    研究成果: Article

    2 引用 (Scopus)

    抄録

    This paper considers a backward problem on a heat equation with a fractional Laplacian. It is not easy to solve a backward heat equation directly. This problem is a well-known ill-posed problem. In order to consider a backward heat equation with a fractional Laplacian, we apply the N-th power of the Dirichlet-Laplacian and small parameters to regularize the equation. This method is called a quasi-reversibility method. We use the generalized quasi-reversibility method to change the backward heat system into another system. This paper shows the existence of a strong solution of the modified backward heat system, and derives L2-estimates of the difference between a solution of the heat equation with the fractional Laplacian and a solution of our system.

    元の言語English
    ページ(範囲)47-57
    ページ数11
    ジャーナルAnalysis
    35
    発行部数1
    DOI
    出版物ステータスPublished - 2015 3 1

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    Quasi-reversibility
    Fractional Laplacian
    Heat Equation
    Heat
    Dirichlet Laplacian
    Ill-posed Problem
    Strong Solution
    Small Parameter
    Hot Temperature
    Estimate

    ASJC Scopus subject areas

    • Applied Mathematics
    • Analysis
    • Numerical Analysis

    これを引用

    Generalized quasi-reversibility method for a backward heat equation with a fractional Laplacian. / Koba, Hajime; Matsuoka, Hideki.

    :: Analysis, 巻 35, 番号 1, 01.03.2015, p. 47-57.

    研究成果: Article

    Koba, Hajime ; Matsuoka, Hideki. / Generalized quasi-reversibility method for a backward heat equation with a fractional Laplacian. :: Analysis. 2015 ; 巻 35, 番号 1. pp. 47-57.
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