Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (1392 KB) | Metadata | Table of Contents | ZAA summary
Published online: 1999-06-30
A Multidimensional Identification Problem Related to a Hyperbolic Integro-Differential EquationAlfredo Lorenzi (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