Partial reconstruction of the source term in a linear parabolic initial problem with Dirichlet boundary conditions

Davide Guidetti

doi:10.3934/dcds.2013.33.5107

Article Contents

2013, Volume 33, Issue 11&12: 5107-5141. Doi: 10.3934/dcds.2013.33.5107

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Partial reconstruction of the source term in a linear parabolic initial problem with Dirichlet boundary conditions

Davide Guidetti^1,

1.
Dipartimento di Matematica, Piazza di Porta S. Donato, 5, 40126 Bologna

Received: September 30, 2011

Revised: July 31, 2012

Published: October 2013

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Abstract

We consider the problem of the reconstruction of the source term in a parabolic Cauchy-Dirichlet system in a cylindrical domain. The supplementary information, necessary to determine the unknown part of the source term together with the solution, is given by the knowledge of an integral of the solution with respect to some of the space variables.

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Mathematics Subject Classification: Primary: 35K20, 35K30; Secondary: 35J25.

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