American Institute of Mathematical Sciences

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March  2009, 8(2): 601-620. doi: 10.3934/cpaa.2009.8.601

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, Italy
2. 

Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy

Received  December 2007 Revised  July 2008 Published  December 2008

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: identification problem, global in time existence and uniqueness result, Strongly damped wave equation with memory.
Mathematics Subject Classification: Primary: 35R30, 45K05, 45N05; Secondary: 80A20.
Citation: Fabrizio Colombo, Davide Guidetti. Identification of the memory kernel in the strongly damped wave equation by a flux condition. Communications on Pure & Applied Analysis, 2009, 8 (2) : 601-620. doi: 10.3934/cpaa.2009.8.601
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