An inverse problem for semilinear equations involving the fractional Laplacian

Abstract

Our work concerns the study of inverse problems of heat and wave equations involving the fractional Laplacian operator with zeroth order nonlinear perturbations. We recover nonlinear terms in the semilinear equations from the knowledge of the fractional Dirichlet-to-Neumann type map combined with the Runge approximation and the unique continuation property of the fractional Laplacian.

Nonlocal problems for a fractional order mixed parabolic equation

“…Also, in [26] Pu-Zhao Kow et al considered the inverse problems of heat and wave equations involving the fractional Laplacian operator with zeroth order nonlinear perturbations and recovered nonlinear terms in the semilinear equations by employing the fractional Dirichlet-to-Neumann type map combined with the Runge approximation and the unique continuation property of the fractional Laplacian. For further discussions in this direction, we refer to [12], [17], [20], and references therein.…”