An inverse problem for semilinear equations involving the fractional Laplacian
PZ Kow, S Ma, SK Sahoo - Inverse Problems, 2023 - iopscience.iop.org
PZ Kow, S Ma, SK Sahoo
Inverse Problems, 2023•iopscience.iop.orgOur 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.
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.
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.
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