We consider a reaction-diffusion equation for the front motion u in which the reaction term is given by c(x)g(u). We formulate a suitable inverse problem for the unknowns u and c, where u satisfies homogeneous Neumann boundary conditions and the additional condition is of integral type on the time interval [0, T]. Uniqueness of the solution is proved in the case of a linear g. Assuming g non linear, we show uniqueness for large T.
IDENTIFYING A SPACE DEPENDENT COEFFICIENT IN A REACTION-DIFFUSION EQUATION / Beretta, Elena; Cecilia, Cavaterra. - In: INVERSE PROBLEMS AND IMAGING. - ISSN 1930-8337. - STAMPA. - 5:2(2011), pp. 285-296. [10.3934/ipi.2011.5.285]
IDENTIFYING A SPACE DEPENDENT COEFFICIENT IN A REACTION-DIFFUSION EQUATION
BERETTA, Elena;
2011
Abstract
We consider a reaction-diffusion equation for the front motion u in which the reaction term is given by c(x)g(u). We formulate a suitable inverse problem for the unknowns u and c, where u satisfies homogeneous Neumann boundary conditions and the additional condition is of integral type on the time interval [0, T]. Uniqueness of the solution is proved in the case of a linear g. Assuming g non linear, we show uniqueness for large T.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
