By means of the Laplace transform method sufficient conditions for the existence of exponentially decaying memory kernels in heat flow and viscoelasticity are derived solving corresponding inverse problems. The observation functionals of the inverse problems are built up by n eigenfunctions of the related elliptic equation or the data of the direct problems possess n non-vanishing Fourier coefficients, only. In the special cases n = 1 and n = 2 the Laplace transforms of the memory kernel are given in explicit form.
Editor-in-Chief: Kabanikhin, Sergey I.
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Identification of exponentially decreasing memory kernels in heat conduction and viscoelasticity by finite-dimensional inverse problems
∗Tallinn Technical University, Institute of Cybernetics, Akadeemia tee 21, 12618 Tallinn, Estonia. E-mail: janno@ioc.ee
†Freiberg University of Mining and Technology, Department of Mathematics and Computer Science, 09599 Freiberg (Sachs), Germany. E-mail: wolfersd@math.tu-freiberg.de
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 13, Issue 1, Pages 65–92, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/1569394053583757,
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