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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 2, 1999, pp. 407–435
DOI: 10.4171/ZAA/890

Published online: 1999-06-30

A Multidimensional Identification Problem Related to a Hyperbolic Integro-Differential Equation

Alfredo Lorenzi[1]

(1) Università degli Studi di Milano, Italy

We prove a global in time existence and uniqueness theorem for the identification of a relaxation kernel h entering a hyperbolic integro- differential 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 integro-differential 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 integro-differential hyperbolic equations, determination of space- and time-dependent relaxation kernels, global existence, uniqueness and continuous dependence results

Lorenzi Alfredo: A Multidimensional Identification Problem Related to a Hyperbolic Integro-Differential Equation. Z. Anal. Anwend. 18 (1999), 407-435. doi: 10.4171/ZAA/890