On the uniqueness of nonlinear diffusion coefficients in the presence of lower order terms

We consider the identification of nonlinear diffusion coefficients of the form a(t,u) or a(u) in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is established under very general assumptions using partial knowledge of the Dirichlet-to-Neumann map. The proof of our...

Full description

Saved in:
Bibliographic Details
Published inInverse problems Vol. 33; no. 11; pp. 115005 - 115020
Main Authors Egger, Herbert, Pietschmann, Jan-Frederik, Schlottbom, Matthias
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.11.2017
Subjects
identifiability
nonlinear diffusion
nonlinear PDE
parameter identification
uniqueness
Online AccessGet full text

Cover

More Information
Summary:We consider the identification of nonlinear diffusion coefficients of the form a(t,u) or a(u) in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is established under very general assumptions using partial knowledge of the Dirichlet-to-Neumann map. The proof of our main result relies on the construction of a series of appropriate Dirichlet data and test functions with a particular singular behavior at the boundary. This allows us to localize the analysis and to separate the principal part of the equation from the remaining terms. We therefore do not require specific knowledge of lower order terms or initial data which allows to apply our results to a variety of applications. This is illustrated by discussing some typical examples in detail.
Bibliography:IP-101323.R1
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/aa8cae