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

This issue Previous Article Boundedness and blowup solutions for quasilinear parabolic systems with lower order terms Next Article Quasilinear Schrödinger equations involving concave and convex nonlinearities

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: November 30, 2007

Revised: June 30, 2008

Published: February 2009

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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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