Abstract and Applied Analysis
Volume 2013 (2013), Article ID 297104, 16 pages
http://dx.doi.org/10.1155/2013/297104
Research Article

Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form

Kairi Kasemets and Jaan Janno

Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia

Received 4 October 2012; Accepted 23 November 2012

Academic Editor: Maurizio Grasselli

Copyright © 2013 Kairi Kasemets and Jaan Janno. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.