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 / E. Beretta, C. Cavaterra. - In: INVERSE PROBLEMS AND IMAGING. - ISSN 1930-8337. - 5:2(2011 May), pp. 285-296. [10.3934/ipi.2011.5.285]
Identifying a space dependent coefficient in a reaction-diffusion equation
C. CavaterraUltimo
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].File | Dimensione | Formato | |
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