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

2 Scopus citations


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
Issue number5
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • General Engineering
  • Computer Science Applications
  • Applied Mathematics


Dive into the research topics of 'Identifying an unknown source term in a heat equation with time-dependent coefficients'. Together they form a unique fingerprint.

Cite this