Identification of memory kernels in general linear heat flow

Identification of memory kernels in general linear heat flow J. Janno and L. V. Wolfersdorf given by the values of two functionals over the temperature. As in our papers [10, 11] we obtain global in time existence of solutions besides uniqueness and stability of solutions. For simplicity, as in [10] we restrict ourselves to the case of continuous memory kernels whereas in [11] (as in the mentioned papers by Lorentzi and Sinestrari) a weakly singular memory kernel of flux is dealt with. But we also deal with the case of a constitutive relation for the heat flux of purely integral type as in the theory of Gurtin and Pipkin [9] (cf. also [[4])2. FORMULATION OF PROBLEM In the general linear theory of heat flow in a rigid isotropic body consisting of material with thermal memory, the following system of constitutive relations holds (cf. [1, 3, 6, 7, 9, 10, 18-22]) e(x, t) = (x) (u(x, t)+ f n(t - }(, r) dr\ (2.1) q(x, t) = -7(x) ( XVu(x, t) - i m(t - r)Vu(x, t) dr\ J -00 (2.2) together with the heat balance equation I^OM) + div £(*,«) - /(x,f), x D (2.3) in bounded domain D of the Euclidian space R p ,p > http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and Ill-Posed Problems de Gruyter

Identification of memory kernels in general linear heat flow

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0928-0219
eISSN
1569-3945
DOI
10.1515/jiip.1998.6.2.141
Publisher site
See Article on Publisher Site

Abstract

J. Janno and L. V. Wolfersdorf given by the values of two functionals over the temperature. As in our papers [10, 11] we obtain global in time existence of solutions besides uniqueness and stability of solutions. For simplicity, as in [10] we restrict ourselves to the case of continuous memory kernels whereas in [11] (as in the mentioned papers by Lorentzi and Sinestrari) a weakly singular memory kernel of flux is dealt with. But we also deal with the case of a constitutive relation for the heat flux of purely integral type as in the theory of Gurtin and Pipkin [9] (cf. also [[4])2. FORMULATION OF PROBLEM In the general linear theory of heat flow in a rigid isotropic body consisting of material with thermal memory, the following system of constitutive relations holds (cf. [1, 3, 6, 7, 9, 10, 18-22]) e(x, t) = (x) (u(x, t)+ f n(t - }(, r) dr\ (2.1) q(x, t) = -7(x) ( XVu(x, t) - i m(t - r)Vu(x, t) dr\ J -00 (2.2) together with the heat balance equation I^OM) + div £(*,«) - /(x,f), x D (2.3) in bounded domain D of the Euclidian space R p ,p >

Journal

Journal of Inverse and Ill-Posed Problemsde Gruyter

Published: Jan 1, 1998

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