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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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An inverse problem for a linearized model in the theory of combustion

Fabrizio Colombo1

1Dipartimento di Matematica, Politecnico di Milano, Via Bonardi n. 9, 20133, Milano, Italy. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 18, Issue 2, Pages 167–187, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2010.006, May 2010

Publication History

Published Online:


In the recent paper [Colombo, Physica D 236: 81–89, 2007] the author investigates an inverse problem arising in the theory of combustion. The problem studied is: determine the temperature u and the convolution memory kernel k in the evolution equation

given suitable initial-boundary conditions and the following additional restriction on u:

Ω φ(x)u(t, x) dx = g(t),

where φ and g are given functions. The main results are a local in time existence theorem and a global in time uniqueness result. In this paper we complete the study considering the linearized version of the model. We prove that, if F(u(t, x), ∇u(t, x)) is sublinear, then the inverse problem has a unique global in time solution.

Keywords.: Inverse problem; parabolic integrodifferential equation; memory kernel; combustion theory; global in time existence and uniqueness result

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