Identifying a space dependent coefficient in a reaction-diffusion equation

Elena Beretta; Cecilia Cavaterra

doi:10.3934/ipi.2011.5.285

Article Contents

2011, Volume 5, Issue 2: 285-296. Doi: 10.3934/ipi.2011.5.285

This issue Previous Article Next Article On an inverse problem in electromagnetism with local data: stability and uniqueness

Identifying a space dependent coefficient in a reaction-diffusion equation

Elena Beretta^1, and
Cecilia Cavaterra^2,

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

Received: February 28, 2010

Revised: August 31, 2010

Published: April 2011

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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.

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References

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