An inverse problem for the fractional porous medium equation

Article type: Research Article

Authors: Li, Li^{; *}

Affiliations: Institute for Pure and Applied Mathematics, University of California, Los Angeles, CA 90095, USA

Correspondence: [*] Corresponding author. E-mail: 1062335412@qq.com.

Abstract: We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the Dirichlet-to-Neumann map. Our approach relies on a time-integral transform technique as well as the unique continuation property of the fractional operator.

Keywords: Inverse problem, fractional porous medium equation, unique continuation property

DOI: 10.3233/ASY-221781

Journal: Asymptotic Analysis, vol. 131, no. 3-4, pp. 583-594, 2023