Computational identification of the lowest space-wise dependent coefficient of a parabolic equation
This work provides a theoretical and numerical method for a specific inverse problem in parabolic PDEs, which is incremental for researchers in inverse problems.
The paper addresses a nonlinear inverse problem of identifying the lowest space-dependent coefficient of a parabolic equation using final time data. An iterative algorithm is proposed, and its monotonic convergence is proven via the maximum principle, with numerical examples for a 2D problem.
In the present work, we consider a nonlinear inverse problem of identifying the lowest coefficient of a parabolic equation. The desired coefficient depends on spatial variables only. Additional information about the solution is given at the final time moment, i.e., we consider the final redefinition. An iterative process is used to evaluate the lowest coefficient, where at each iteration we solve the standard initial-boundary value problem for the parabolic equation. On the basis of the maximum principle for the solution of the differential problem, the monotonicity of the iterative process is established along with the fact that the coefficient approaches from above. The possibilities of the proposed computational algorithm are illustrated by numerical examples for a model two-dimensional problem.