Annali di Matematica Pura ed Applicata

, Volume 193, Issue 3, pp 779–816 | Cite as

Identification of a convolution kernel in a control problem for the heat equation with a boundary memory term

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Abstract

We consider the evolution of the temperature \(u\) in a material with thermal memory characterized by a time-dependent convolution kernel \(h\). The material occupies a bounded region \(\Omega \) with a feedback device controlling the external temperature located on the boundary \(\Gamma \). Assuming both \(u\) and \(h\) unknown, we formulate an inverse control problem for an integrodifferential equation with a nonlinear and nonlocal boundary condition. Existence and uniqueness results of a solution to the inverse problem are proved.

Keywords

Integrodifferential equations Automatic control problems Inverse problems 

Mathematics Subject Classification (2010)

35R30 35K20 45K05 47J040 93B52 
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© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  2. 2.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

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