Abstract

We consider the bistable equation vt - ? v = f (v, x), f (v, x) = a (x) v (1 - v) (v - a (x)) with homogeneous Neumann boundary conditions in a bounded domain O ? R3 with regular boundary. For this equation, we prove Lipschitz stability for the inverse problem of recovering parameters a and a from measurements of v in (0, T) × ?, where ? is an arbitrary nonempty open subset of O and measurements of v (t0) in the whole domain O at some positive time t0 such that 0 < t0 < 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). © 2009 Académie des sciences.