A positivity principle for parabolicintegro-differential equations and  inverse problems with final overdetermination

Jaan Janno; Kairi Kasemets

doi:10.3934/ipi.2009.3.17

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2009, Volume 3, Issue 1: 17-41. Doi: 10.3934/ipi.2009.3.17

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A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination

Jaan Janno^1, and
Kairi Kasemets^2,

1.
Institute of Cybernetics and Institute of Mathematics, Tallinn University of Technology, Akadeemia tee 21, Tallinn, 12618
2.
Institute of Mathematics, Tallinn University of Technology, Ehitajate tee 5, Tallinn, 12618

Received: June 2008

Revised: January 2009

Published: February 2009

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Abstract

A positivity principle for parabolic integro-differential equations is proved. By means of this principle, uniqueness, existence and stability for an inverse source problem and two inverse coefficient problems are established.

Keywords:

parabolic integro-differential equation,
extremum principle,
inverse problem,
final overdetermination.

Mathematics Subject Classification: 35B50, 35R30.

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