Some inverse stability results for the bistable reaction-diffusion equation using Carleman inequalities

We consider the bistable equation nu(t) - Delta nu = f (nu, x), f(nu,x) = a (x)nu(1 - nu) (nu - alpha(x)) with homogeneous Neumann boundary conditions in a bounded domain Omega subset of R(3) with regular boundary. For this equation, we prove Lipschitz stability for the inverse problem of recovering parameters a and a from measurements of nu in (0, T) x omega, where omega is an arbitrary nonempty open subset of Omega and measurements of nu(t(0)) in the whole domain Omega at some positive time t(0) such that 0 < t(0) < T. The result is based in some suitable global Carleman estimate for the nonlinear problem. To cite this article: M. Boulakia et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.