Identification of the memory kernel in the strongly damped wave equation by a flux condition

Fabrizio Colombo; Davide Guidetti

doi:10.3934/cpaa.2009.8.601

Article Contents

2009, Volume 8, Issue 2: 601-620. Doi: 10.3934/cpaa.2009.8.601

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Identification of the memory kernel in the strongly damped wave equation by a flux condition

Fabrizio Colombo^1, and
Davide Guidetti^2,

1.
Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano
2.
Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna

Received: December 2007

Revised: July 2008

Published: March 2009

Abstract / Introduction Related Papers Cited by

Abstract

We study an abstract inverse problem of reconstruction of the solution of a semilinear mixed integrodifferential parabolic problem, together with a convolution kernel. The supplementary information required to solve the problem also involves a convolution term with the same unknown kernel. The abstract results are applicable to the identification of a memory kernel in a strongly damped wave equation using a flux condition.

Keywords:

Strongly damped wave equation with memory,
identification problem,
global in time existence and uniqueness result.

Mathematics Subject Classification: Primary: 35R30, 45K05, 45N05; Secondary: 80A20.

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