A non-isothermal Ginzburg–Landau model in superconductivity: Existence,uniqueness and asymptotic behaviour |
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Authors: | Valeria Berti Mauro Fabrizio |
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Affiliation: | Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy |
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Abstract: | In this paper we study a Ginzburg–Landau model which describes the behaviour of a superconducting material including thermal effects. We extend the traditional formulation of the problem, by introducing the temperature as an additional state variable. Accordingly, together with the Gor’kov–Eliashberg system, we introduce an evolution equation for the absolute temperature. We examine in detail the case which allows only variations of the concentration of superconducting electrons and of the temperature, neglecting the electromagnetic field. For this problem existence and uniqueness of the solution are shown. Finally we analyze the asymptotic behaviour of the solutions, proving that the system possesses a global attractor. |
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Keywords: | 82D55 35B41 |
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