Identification of a nonlinear parameter in a parabolic equation from a linear equation
type: Item
instance of: scholarly article
title: Identification of a nonlinear parameter in a parabolic equation from a linear equation
zbMATH Open document ID: 0845.93018
author: Yanyan Li
published in: Computational and Applied Mathematics
publication date: 1996-05-29T00:00:00Z
review text: The nonlinear parabolic system of the form: \[ \begin{cases} {\partial u \over \partial t} - \nabla \bigl( a(u) \nabla u \bigr) = f(x,t) \\ a(u) {\partial u \over \partial n} = g(x,t) \\ u(x, 0) = u_0 (x) \end{cases} \tag{1} \] is considered. The problem consists in finding the nonlinear parameter \(a(u)\) when an information about the state solution \(u\) of (1) is known. Results on existence are first given. Then, the identification problem and its error estimate is studied. \(\Lambda\) penalized functional is introduced and the identification of the nonlinear parameter is simplified by replacing this parameter with a linear one. Numerical approximation and test results are finally given.
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 863608
zbMATH Keywords: nonlinear
zbMATH Keywords: parabolic system
zbMATH Keywords: identification
reviewed by: Yves Cherruault
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 863608