Electron. J. Diff. Equ., Vol. 2014 (2014), No. 176, pp. 1-19.

Weak inverse problems for parabolic integro-differential equations containing two kernels

Kairi Kasemets, Jaan Janno

Abstract:
An inverse problem to determine a coefficient and two kernels in a parabolic integro-differential equation is considered. A corresponding direct problem is supposed to be in the weak form. Existence of the quasi-solution is proved and issues related to Frechet differentiation of the cost functional are treated.

Submitted April 8, 2014. Published August 15, 2014.
Math Subject Classifications: 35R30, 80A23.
Key Words: Inverse problem; parabolic integro-differential equation; relaxation kernel; quasi-solution.

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Kairi Kasemets
Tallinn University of Technology
Ehitajate tee 5, Tallinn, Estonia
email: kairi.kasemets@ttu.ee
Jaan Janno
Tallinn University of Technology
Ehitajate tee 5, Tallinn, Estonia
email: janno@ioc.ee

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