Recovery of a potential coefficient in a pseudoparabolic system from nonlocal observation

Abstract

We consider a nonlinear inverse problem for identifying an unknown time-dependent potential coefficient in a linear pseudoparabolic equation from nonlocal inversion input, which is quite different from the cases of parabolic equation due to the appearance of the mixed derivatives of third order in the governed equation. Based on the established positive property of the solution to the direct problem, the uniqueness and the Lipschitz conditional stability of this inverse problem are addressed by the principle of contraction mappings for specially chosen weight function in the average observation input data. Then, in terms of the fixed point equation, an iterative algorithm is established to construct the approximate solution to this inverse problem with explicit error estimate, which also leads to the optimal error bounds for specified choice strategy of the iteration times. Some numerical results are presented to validate our proposed reconstruction scheme.