Quasi Solution of a Nonlinear Inverse Parabolic Problem

@article{Shayegan2019QuasiSO,
  title={Quasi Solution of a Nonlinear Inverse Parabolic Problem},
  author={Amir Hossein Salehi Shayegan and Ali Zakeri and Touraj Nikazad},
  journal={Bulletin of the Iranian Mathematical Society},
  year={2019},
  volume={45},
  pages={1-12}
}
In this paper, we study the existence of a quasi solution to nonlinear inverse parabolic problem related to $$ \aleph (u):\equiv u_{t}-\nabla \cdot (F(x,\nabla u)) $$ℵ(u):≡ut-∇·(F(x,∇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… CONTINUE READING