Identifying an unknown source term in a heat equation with time-dependent coefficients

Nguyen Van Duc, Luong Duy Nhat Minh, Nguyen Trung Thanh

    Research output: Contribution to journalArticlepeer-review

    1 Scopus citations

    Abstract

    An inverse source problem for an n-dimensional heat equation with a time-varying coefficient is investigated. The spatially dependent component of a source function is determined from a measurement at the final time. The inverse problem is regularized by a mollification method. Hölder-type stability estimates are proved. Error estimates of Hölder type are also proved for regularized solutions for both a priori and a posteriori mollification parameter choice rules. A non-iterative reconstruction algorithm is proposed. Numerical examples in one and two dimensions are shown to illustrate the performance of the proposed method.

    Original languageEnglish (US)
    Pages (from-to)609-635
    Number of pages27
    JournalInverse Problems in Science and Engineering
    Volume29
    Issue number5
    DOIs
    StatePublished - 2021

    All Science Journal Classification (ASJC) codes

    • Engineering(all)
    • Computer Science Applications
    • Applied Mathematics

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