Existence and uniqueness results for an inverse problem for a semilinear equation with final overdetermination

In the present paper, unique solvability of a source identification inverse problem for a semilinear equation with a final overdetermination in a Banach space is investigated. Moreover, the first order of accuracy Rothe difference scheme is presented for numerically solving this problem. The existence and uniqueness result for this difference scheme is given. The efficiency of the proposed method is evaluated by means of computational experiments. © 2018, University of Nis. All rights reserved.

Authors
Sazaklioglu A.U. 1, 2 , Erdogan A.S. 3 , Ashyralyev A. 4, 5, 6
Journal
Filomat
Publisher
University of Nis
Issue number
3
Language
English
Pages
847-858
State
Published
Link
External link
DOI
10.2298/FIL1803847S
Volume
32
Year
2018
Organizations
  • 1 Department of Astronautical Engineering, University of Turkish Aeronautical Association, Ankara, 06790, Turkey
  • 2 Department of Mathematics, Istanbul University, Istanbul, 34452, Turkey
  • 3 Sigma Labs, Satbayev University, Almaty, 050013, Kazakhstan
  • 4 Department of Mathematics, Near East University, Mersin 10, Nicosia, Turkey
  • 5 Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
  • 6 Peoples’ Friendship University of Russia, Moscow, 117198, Russian Federation
Keywords
Existence; Finite difference method; Inverse problem; Semilinear parabolic equations; Uniqueness
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