A uniqueness result for the identification of a time-dependent diffusion coefficient



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Fraguela, A. and Infante del Río, Juan Antonio and Ramos del Olmo, Ángel Manuel and Rey Cabezas, Jose María (2013) A uniqueness result for the identification of a time-dependent diffusion coefficient. Inverse problems, 29 (12). ISSN 0266-5611

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Official URL: http://iopscience.iop.org/0266-5611/29/12/125009/pdf/0266-5611_29_12_125009.pdf


This paper deals with the problem of determining the time-dependent thermal diffusivity coefficient of a medium, when the evolution of the temperature in a part of it is known. Such situations arise in the context of food technology, when thermal processes at high pressures are used for extending the shelf life of the food, in order to preserve its nutritional and organoleptic properties (Infante et al 2009 On the Modelling and Simulation of High Pressure Processes and Inactivation of Enzymes in Food Engineering pp 2203–29 and Otero et al 2007 J. Food Eng. 78 1463–70). The phenomenon is modeled by the heat equation involving a term which depends on the source temperature and pressure increase, and appropriate initial and boundary conditions. We study the inverse problem of determining time-dependent thermal diffusivities k, when some temperature measurements at the border and inside the medium are known. We prove the uniqueness of the inverse problem solution under suitable a priori assumptions on regularity, size and growth of k.

Item Type:Article
Uncontrolled Keywords:Inverse problems; Thermodynamic functions and equations of state; Thermal diffusivity; Transport processes
Subjects:Sciences > Physics > Mathematical physics
ID Code:23748
Deposited On:28 Nov 2013 11:39
Last Modified:12 Dec 2018 15:06

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