Numerical reconstruction based on Carleman estimates of a source term in a reaction–diffusion equation

• Published in: ESAIM. Control, optimisation and calculus of variations Vol. 27; p. S27
• Main Authors: Boulakia, Muriel, de Buhan, Maya, Schwindt, Erica L.
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 2021
• Subjects: Analysis of PDEs; Convergence; Iterative algorithms; Iterative methods; Mathematics; Reaction-diffusion equations; Reconstruction; Numerical reconstruction; Inverse problems; 93B07; Carleman estimates; numerical reconstruction AMS subject classifications: 35R30; 35K57; 35K55; Nonlinear parabolic equations

In this article, we consider a reaction–diffusion equation where the reaction term is given by a cubic function and we are interested in the numerical reconstruction of the time-independent part of the source term from measurements of the solution. For this identification problem, we present an iter...