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

Hajime Koba, Hideki Matsuoka

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)47-57
    Number of pages11
    JournalAnalysis
    Volume35
    Issue number1
    DOIs
    Publication statusPublished - 2015 Mar 1

    Fingerprint

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

    Keywords

    • 35K05
    • Primary 35R30
    • secondary 35R25

    ASJC Scopus subject areas

    • Applied Mathematics
    • Analysis
    • Numerical Analysis

    Cite this

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

    In: Analysis, Vol. 35, No. 1, 01.03.2015, p. 47-57.

    Research output: Contribution to journalArticle

    Koba, Hajime ; Matsuoka, Hideki. / Generalized quasi-reversibility method for a backward heat equation with a fractional Laplacian. In: Analysis. 2015 ; Vol. 35, No. 1. pp. 47-57.
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