Identifying a space dependent coefficient in a reaction-diffusion equation

Pages: 285 - 296, Volume 5, Issue 2, May 2011

doi:10.3934/ipi.2011.5.285       Abstract        References        Full Text (331.2K)       Related Articles

Elena Beretta - Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le Aldo Moro 5, 00185 Roma, Italy (email)
Cecilia Cavaterra - Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, 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.
Mathematics Subject Classification:  Primary: 35R30; Secondary: 35K57.

Received: March 2010;      Revised: September 2010;      Published: May 2011.

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