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Identifying an unknown source term in a heat equation with time-dependent coefficients
Authors: Nguyen Van Duc, Luong Duy Nhat Minh, Nguyen Trung Thanh
293    0
Inverse Problems in Science and Engineering
: 29/5     : 609-635
: https://www.tandfonline.com/doi/full/10.1080/17415977.2020.1798421
Publishing year: 5/2021
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 noniterative reconstruction algorithm is proposed. Numerical examples in one and two dimensions are shown to illustrate the performance of the proposed method.
Inverse source problem; heat equation; stability estimates; mollification method; numerics
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