Identifying a space dependent coefficient in a reaction-diffusion equation

Elena Beretta, Cecilia Cavaterra

Research output: Contribution to journalArticle

Abstract

We consider a reaction-difiusion equation for the front motion u in which the reaction term is given by c(x)g(u). We formulate a suitable inverse problem for the unknowns u and c, where u satisfies homogeneous Neumann boundary conditions and the additional condition is of integral type on the time interval [0; T]. Uniqueness of the solution is proved in the case of a linear g. Assuming g non linear, we show uniqueness for large T.

Original languageEnglish (US)
Pages (from-to)285-296
Number of pages12
JournalInverse Problems and Imaging
Volume5
Issue number2
DOIs
StatePublished - May 1 2011

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Reaction-diffusion Equations
Inverse problems
Uniqueness
Boundary conditions
Dependent
Coefficient
Neumann Boundary Conditions
Inverse Problem
Unknown
Interval
Motion
Term

Keywords

  • Inverse problems
  • Reaction-difiusion equations

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

Cite this

Identifying a space dependent coefficient in a reaction-diffusion equation. / Beretta, Elena; Cavaterra, Cecilia.

In: Inverse Problems and Imaging, Vol. 5, No. 2, 01.05.2011, p. 285-296.

Research output: Contribution to journalArticle

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