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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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Global in time results for a class of inverse problems

F. Colombo1

1Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 3, Pages 259–287, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.019, April 2009

Publication History

Received:
2008-01-23
Revised:
2008-04-21
Published Online:
2009-04-16

Abstract

We show a strategy recently developed to prove global in time existence and uniqueness results for integrodifferential inverse problems. The models we discuss in this paper are:

which are: the strongly damped wave equation with memory, the heat equation with memory and a model in the theory of combustion with memory, respectively. Here f is a given nonlinear function and Ω is a bounded domain in ℝ3. We determine u and the convolution memory kernel h under suitable initial–boundary conditions and assuming to know an additional restriction on the state variable u, for example of type

where φ and g are given functions representing the type of device used to measure u.

Key words.: Heat equation with memory; combustion model with memory; strongly damped wave equation with memory; identification problem; global in time existence and uniqueness result

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