An introduction to the mathematical theory of inverse problems
An introduction to the mathematical theory of inverse problems
Determination of a control function in three-dimensional parabolic equations
Mathematics and Computers in Simulation
Solving an inverse parabolic problem by optimization from final measurement data
Journal of Computational and Applied Mathematics
Determination of a spacewise dependent heat source
Journal of Computational and Applied Mathematics
Identifying the coefficient of first-order in parabolic equation from final measurement data
Mathematics and Computers in Simulation
Determination of the source parameter in a heat equation with a non-local boundary condition
Journal of Computational and Applied Mathematics
Source term identification in 1-D IHCP
Computers & Mathematics with Applications
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This work studies an inverse problem of determining the first-order coefficient of degenerate parabolic equations using the measurement data specified at a fixed internal point. Being different from other ordinary parameter identification problems in parabolic equations, in our mathematical model there exists degeneracy on the lateral boundaries of the domain, which may cause the corresponding boundary conditions to go missing. By the contraction mapping principle, the uniqueness of the solution for the inverse problem is proved. A numerical algorithm on the basis of the predictor-corrector method is designed to obtain the numerical solution and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown function is recovered very well. The results obtained in the paper are interesting and useful, and can be extended to other more general inverse coefficient problems of degenerate PDEs.