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;
2011-01-01
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.File in questo prodotto:
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