Identification of a special class of memory kernels in one-dimensional heat flow

J. Janno 1  and L.V. Wolfersdorf 2
  • 1 Institute of Cybernetics, Tallinn Technical University, 12618 Tallinn, Estonia.
  • 2 Faculty of Mathematics and Computer Science, Freiberg University of Mining and Technology, D-09596 Freiberg, Germany.

Abstract

- We consider the inverse problem of identification of memory kernels in one-dimensional heat flow are dealt with where the kernel is represented by a finite sum of products of known spatially-dependent functions and unknown time-dependent functions. As additional conditions for the inverse problems observations of both heat flux and temperature are prescribed. Using the Laplace transform method we prove an existence and uniqueness theorem for the memory kernel.

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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.

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