Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 2, pp. 407  435 (1999) 

A Multidimensional Identification Problem Related to a Hyperbolic IntegroDifferential EquationA. LorenziUniversità degli Studi, Dept. Math., via Saldini 50, 20133 Milano, ItaliaAbstract: We prove a global in time existence and uniqueness theorem for the identification of a relaxation kernel $h$ entering a hyperbolic integrodifferential equation, related to a convex cylinder with a smooth lateral surface, when the coefficient $h$ is assumed to depend on time and one space variable and general additional conditions are provided. A continuous dependence result for the identification problem is also stated. Finally, a separate proof concerning the existence and uniqueness of the solution to the related direct integrodifferential problem is also given in a suitable functional space. Moreover, the dependence of such a solution with respect to the relaxation kernel is fully analysed. Keywords: linear integrodifferential hyperbolic equations, determination of space and timedependent relaxation kernels, global existence, uniqueness and continuous dependence results Full text of the article:
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