Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 1, pp 1–12 | Cite as

Quasi Solution of a Nonlinear Inverse Parabolic Problem

  • Amir Hossein Salehi Shayegan
  • Ali Zakeri
  • Touraj NikazadEmail author
Original Paper


In this paper, we study the existence of a quasi solution to nonlinear inverse parabolic problem related to \( \aleph (u):\equiv u_{t}-\nabla \cdot (F(x,\nabla u)) \) where the function F is unknown. We consider a methodology, involving minimization of a least squares cost functional, to identify the unknown function F. At the first step of the methodology, we give a stability result corresponding to connectivity of F and u which leads to the continuity of the cost functional. We next construct an appropriate class of admissible functions and show that a solution of the minimization problem exists for the continuous cost functional. At the last step, we conclude that the nonlinear inverse parabolic problem has at least one quasi solution in that class of functions.


Quasi solution Nonlinear inverse parabolic problem Time-dependent problems 

Mathematics Subject Classification

Primary 35K55 Secondary 35R30 49J20 



We wish to thank two anonymous referees for constructive criticism and helpful suggestions which improved our paper.


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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  • Amir Hossein Salehi Shayegan
    • 1
  • Ali Zakeri
    • 1
  • Touraj Nikazad
    • 2
    Email author
  1. 1.Faculty of MathematicsK. N. Toosi University of TechnologyTehranIran
  2. 2.School of MathematicsIran University of Science and TechnologyTehranIran

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