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February  2009, 3(1): 17-41. doi: 10.3934/ipi.2009.3.17

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, Estonia
2. 

Institute of Mathematics, Tallinn University of Technology, Ehitajate tee 5, Tallinn, 12618, Estonia

Received  June 2008 Revised  January 2009 Published  February 2009

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: final overdetermination., inverse problem, parabolic integro-differential equation, extremum principle.
Mathematics Subject Classification: 35B50, 35R3.
Citation: Jaan Janno, Kairi Kasemets. A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination. Inverse Problems & Imaging, 2009, 3 (1) : 17-41. doi: 10.3934/ipi.2009.3.17
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