Journal
ADVANCES IN COMPUTATIONAL MATHEMATICS
Volume 46, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/s10444-020-09796-w
Keywords
Two-dimensional sideways heat equation; Kernel regularization method; Stable estimate; Holder-type error estimates
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Funding
- Institute for Computational Science and Technology (ICST), Ho Chi Minh City
- Department of Science and Technology, Ho Chi Minh City [456/QD-KHCNTT]
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We investigate an inverse and ill-posed problem for the two-dimensional inhomogeneous heat equation in the presence of a general source term. The goal here consists of recovering not only the temperature distribution but also the thermal flux from the measure data. With the appearance of the general source term, this model gets far worse than its homogeneous counterpart. Based on an analysis of the instability caused in the solution, we propose a kernel regularization scheme to stabilize the investigated problem. The Holder-type convergence estimates are achieved under some appropriate a priori assumptions. We further numerically demonstrate the theoretical results by proposing a robust algorithm based on the 2-D fast Fourier transform. The numerical outputs exemplify the feasibility and efficiency of the proposed method.
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