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

Boulakia M; Grandmont C; Osses A.

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.

Más información

Título según WOS: Some inverse stability results for the bistable reaction-diffusion equation using Carleman inequalities
Título según SCOPUS: Some inverse stability results for the bistable reaction-diffusion equation using Carleman inequalities
Título de la Revista: COMPTES RENDUS MATHEMATIQUE
Volumen: 347
Número: 11-dic
Editorial: ACAD SCIENCES
Fecha de publicación: 2009
Página de inicio: 619
Página final: 622
Idioma: English
URL: http://linkinghub.elsevier.com/retrieve/pii/S1631073X09001241
DOI:

10.1016/j.crma.2009.03.022

Notas: ISI, SCOPUS