An inverse problem involving two coefficients in a nonlinear reaction-diffusion equation

Michel M. Cristofol (1) , Lionel L. Rogues (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 BioSP - Biostatistique et Processus Spatiaux

This Note deals with a uniqueness and stability result for a nonlinear reaction-diffusion equation with heterogeneous coefficients, which arises as a model of population dynamics in heterogeneous environments. We obtain a Lipschitz stability inequality which implies that two non-constant coefficients of the equation, which can be respectively interpreted as intrinsic growth rate and intraspecific competition coefficients, are uniquely determined by the knowledge of the solution on the whole domain at two times t(0) and t(1) and on a subdomain during a time interval which contains to and t(1). This inequality can be used to reconstruct the coefficients of the equation using only partial measurements of its solution. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Mots clés: species persistence; nonlinear reaction-diffusion equation

Domaines: Equations aux dérivées partielles [math.AP]

Michel M. Cristofol, Lionel L. Rogues. An inverse problem involving two coefficients in a nonlinear reaction-diffusion equation. Comptes Rendus. Mathématique, 2012, 350 (9-10), pp.469-473. ⟨10.1016/j.crma.2012.04.019⟩. ⟨hal-02651929⟩