Identifying an unknown source term in a time-space fractional parabolic equation

Nguyen Van Thang, Nguyen Van Duc, Luong Duy Nhat Minh, Nguyen Trung Thành

    Research output: Contribution to journalArticlepeer-review

    Abstract

    An inverse problem of identifying an unknown space-dependent source term in a time-space fractional parabolic equation is considered in this paper. Under reasonable boundedness assumptions about the source function, a Hölder-type stability estimate of optimal order is proved. To regularize the inverse source problem, a mollification regularization method is applied. Error estimates of the regularized solution are proved for both a priori and a posteriori rules for choosing the mollification parameter. A direct numerical method for solving the regularized problem is proposed and numerical examples are presented to illustrate its effectiveness.

    Original languageEnglish (US)
    Pages (from-to)313-332
    Number of pages20
    JournalApplied Numerical Mathematics
    Volume166
    DOIs
    StatePublished - Aug 2021

    All Science Journal Classification (ASJC) codes

    • Numerical Analysis
    • Computational Mathematics
    • Applied Mathematics

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