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 journalArticle


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)
JournalInverse Problems in Science and Engineering
StateAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

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

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