American Institute of Mathematical Sciences

May  2011, 5(2): 285-296. doi: 10.3934/ipi.2011.5.285

Identifying a space dependent coefficient in a reaction-diffusion equation

 1 Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le Aldo Moro 5, 00185 Roma, Italy 2 Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy

Received  March 2010 Revised  September 2010 Published  May 2011

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 $T$.
Citation: Elena Beretta, Cecilia Cavaterra. Identifying a space dependent coefficient in a reaction-diffusion equation. Inverse Problems & Imaging, 2011, 5 (2) : 285-296. doi: 10.3934/ipi.2011.5.285
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