This article is devoted to the long-term dynamics of a parabolic-hyperbolic system arising in superconductivity. In the literature, the existence and uniqueness of the solution have been investigated but, to our knowledge, no asymptotic result is available. For the bi-dimensional model we prove that the system generates a dissipative semigroup in a proper phase-space where it possesses a (regular) global attractor. Then, we show the existence of an exponential attractor whose basin of attraction coincides with the whole phase-space. Thus, in particular, this exponential attractor contains the global attractor which, as a consequence, is of finite fractal dimension.

Parabolic-hyperbolic time-dependent Ginzburg-Landau-Maxwell equations / Berti, V; Gatti, Stefania. - In: QUARTERLY OF APPLIED MATHEMATICS. - ISSN 0033-569X. - STAMPA. - 64:(2006), pp. 617-639.

Parabolic-hyperbolic time-dependent Ginzburg-Landau-Maxwell equations

GATTI, Stefania
2006

Abstract

This article is devoted to the long-term dynamics of a parabolic-hyperbolic system arising in superconductivity. In the literature, the existence and uniqueness of the solution have been investigated but, to our knowledge, no asymptotic result is available. For the bi-dimensional model we prove that the system generates a dissipative semigroup in a proper phase-space where it possesses a (regular) global attractor. Then, we show the existence of an exponential attractor whose basin of attraction coincides with the whole phase-space. Thus, in particular, this exponential attractor contains the global attractor which, as a consequence, is of finite fractal dimension.
64
617
639
Parabolic-hyperbolic time-dependent Ginzburg-Landau-Maxwell equations / Berti, V; Gatti, Stefania. - In: QUARTERLY OF APPLIED MATHEMATICS. - ISSN 0033-569X. - STAMPA. - 64:(2006), pp. 617-639.
Berti, V; Gatti, Stefania
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/453687
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