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2013 | 11 | 9 | 1651-1676
Tytuł artykułu

Global and exponential attractors for a Caginalp type phase-field problem

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EN
We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.
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Bibliografia
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  • [10] Cherfils L., Miranville A., On the Caginalp system with dynamic boundary conditions and singular potentials, Appl. Math., 2009, 54(2), 89–115 http://dx.doi.org/10.1007/s10492-009-0008-6
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  • [22] Miranville A., Quintanilla R., A generalization of the Caginalp phase-field system based on the Cattaneo law, Nonlinear Anal., 2009, 71(5–6), 2278–2290 http://dx.doi.org/10.1016/j.na.2009.01.061
  • [23] Miranville A., Quintanilla R., Some generalizations of the Caginalp phase-field system, Appl. Anal., 2009, 88(6), 897–894 http://dx.doi.org/10.1080/00036810903042182
  • [24] Miranville A., Quintanilla R., A Caginalp phase-field system with a nonlinear coupling, Nonlinear Anal. Real World Appl., 2010, 11(4), 2849–2861 http://dx.doi.org/10.1016/j.nonrwa.2009.10.008
  • [25] Miranville A., Zelik S., Attractors for dissipative partial differential equations in bounded and unbounded domains, In: Handbook of Differential Equations: Evolutionary Equations, IV, Handb. Diff. Equ., Elsevier/North-Holland, Amsterdam, 2008, 103–200 http://dx.doi.org/10.1016/S1874-5717(08)00003-0
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0258-0
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