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 and and on a subdomain during a time interval which contains and . This inequality can be used to reconstruct the coefficients of the equation using only partial measurements of its solution.
Dans cette Note, nous présentons un résultat dʼunicité et de stabilité pour une équation de réaction–diffusion non linéaire et à coefficients hétérogènes, intervenant notamment dans des modèles de dynamique des populations. Nous établissons une inégalité du type Lipschitz impliquant que la connaissance de la solution de lʼéquation sur tout le domaine dʼétude à des temps et , ainsi que sa connaissance sur un sous-domaine durant un intervalle de temps contenant et , détermine de façon unique deux coefficients hétérogènes de lʼéquation.
Accepted:
Published online:
Michel Cristofol 1; Lionel Roques 2
@article{CRMATH_2012__350_9-10_469_0, author = {Michel Cristofol and Lionel Roques}, title = {An inverse problem involving two coefficients in a nonlinear reaction{\textendash}diffusion equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {469--473}, publisher = {Elsevier}, volume = {350}, number = {9-10}, year = {2012}, doi = {10.1016/j.crma.2012.04.019}, language = {en}, }
TY - JOUR AU - Michel Cristofol AU - Lionel Roques TI - An inverse problem involving two coefficients in a nonlinear reaction–diffusion equation JO - Comptes Rendus. Mathématique PY - 2012 SP - 469 EP - 473 VL - 350 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2012.04.019 LA - en ID - CRMATH_2012__350_9-10_469_0 ER -
Michel Cristofol; Lionel Roques. An inverse problem involving two coefficients in a nonlinear reaction–diffusion equation. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 469-473. doi : 10.1016/j.crma.2012.04.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.019/
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