2026/07/24 by Barbara Kaltenbacher, William Rundell
paper · doi:10.1088/1361-6420/ae9002
Abstract We consider a (sub)diffusion equation with a nonlinearity of the form pf (u)qu, where p and q are space dependent functions. Prominent examples are the Fisher-KPP, the Frank-Kamenetskii-Zeldovich and the Allen-Cahn equations. We devise a fixed point scheme for reconstructing the spatially varying coefficients from interior observations a) at final time under two different excitations b) at two different time instances under a single excitation. Convergence of the scheme as well as local uniqueness of these coefficients is proven. Numerical experiments illustrate the performance of the reconstruction scheme.