Identifying an unknown source term in a heat
equation with time-dependent coefficients
Tác giả: Nguyen Van Duc, Luong Duy Nhat Minh, Nguyen Trung Thanh
Inverse Problems in Science and Engineering
Quyển: 29/5 Trang: 609-635
Năm xuất bản: 5/2021
Tóm tắt
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.
Từ khóa
Inverse source problem; heat equation; stability estimates; mollification method; numerics
