Unique continuation and continuous dependence results for a severely ill-posed integrodifferential parabolic problem with a memory term in the principal part of the differential operator

Alfredo Lorenzi; Francesca Messina

doi:10.1515/jip-2012-0047

Published by De Gruyter April 3, 2013

Unique continuation and continuous dependence results for a severely ill-posed integrodifferential parabolic problem with a memory term in the principal part of the differential operator

Alfredo Lorenzi and Francesca Messina

From the journal Journal of Inverse and Ill-Posed Problems

https://doi.org/10.1515/jip-2012-0047

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Abstract.

We prove uniqueness and continuous dependence results for a severely ill-posed linear integrodifferential boundary-value parabolic problem with no initial condition. This latter condition is replaced with an additional boundary information prescribing the temperature on an open subset of the geometric domain

The integral operators entering the equation are defined by integrals of Volterra type with respect to time. In particular, the class of integrodifferential equations dealt with in this paper include those occurring in the linear theory of heat flow in a rigid body consisting of a material with thermal memory.

Keywords: Ill-posed problems; linear parabolic integrodifferential equations; no initial conditions; uniqueness; approximation results

Received: 2012-06-20

Published Online: 2013-04-03

Published in Print: 2013-04-01

Unique continuation and continuous dependence results for a severely ill-posed integrodifferential parabolic problem with a memory term in the principal part of the differential operator

Abstract.

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