Lipschitz stability for the growth rate coefficients in a nonlinear Fisher-KPP equation

Abstract

We consider a reaction-diffusion model of biological invasion in which the evolution of the population is governed by several parameters among them the intrinsic growth rate \begin{document}$ \mu(x) $\end{document} . The knowledge of this growth rate is essential to predict the evolution of the population, but it is a priori unknown for exotic invasive species. We prove uniqueness and unconditional Lipschitz stability for the corresponding inverse problem, taking advantage of the positivity of the solution inside the spatial domain and studying its behaviour near the boundary with maximum principles. Our results complement previous works by Cristofol and Roques [ 11 , 13 ].