Identifying a space dependent coefficient in a reaction-diffusion equation
Elena Beretta - Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le Aldo Moro 5, 00185 Roma, Italy (email)
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 $T$.
Keywords: Inverse problems, reaction-diffusion equations.
Received: March 2010; Revised: September 2010; Published: May 2011.
2011 Impact Factor1.074