Quasi Solution of a Nonlinear Inverse Parabolic Problem

• Published in: Bulletin of the Iranian Mathematical Society Vol. 45; no. 1; pp. 1 - 12
• Main Authors: Shayegan, Amir Hossein Salehi, Zakeri, Ali, Nikazad, Touraj
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 07.02.2019
• Subjects: Mathematics; Mathematics and Statistics; Original Paper; Primary 35K55; Quasi solution; Time-dependent problems; Nonlinear inverse parabolic problem; 49J20; Secondary 35R30

In this paper, we study the existence of a quasi solution to nonlinear inverse parabolic problem related to ℵ ( u ) : ≡ u t - ∇ · ( 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...