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Título:
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On a Caginalp phase-field system with two temperatures and memory
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Autor/a:
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Conti, Monica; Gatti, Stefania; Miranville, Alain; Quintanilla de Latorre, Ramón
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada |
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Abstract:
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The final publication is available at Springer via https://doi.org/10.1007/s00032-017-0263-z |
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Abstract:
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The Caginalp phase-field system has been proposed in [4] as a simple mathematical model for phase transition phenomena. In this paper, we are concerned with a generalization of this system based on the Gurtin-Pipkin law with two temperatures for heat conduction with memory, apt to describe transition phenomena in nonsimple materials. The model consists of a parabolic equation governing the order parameter which is linearly coupled with a nonclassical integrodifferential equation ruling the evolution of the thermodynamic temperature of the material. Our aim is to construct a robust family of exponential attractors for the associated semigroup, showing the stability of the system with respect to the collapse of the memory kernel. We also study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist. |
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Abstract:
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Peer Reviewed |
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Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
-Thermoelasticity
-Caginalp system
-Two temperatures
-Gurtin-Pipkin law
-Dissipativity
-Exponential attractor stability
-Termoelasticitat
-Equacions diferencials parcials
-Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
-Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
-Classificació AMS::35 Partial differential equations::35L Partial differential equations of hyperbolic type
-Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer |
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Derechos:
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Tipo de documento:
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Artículo - Versión publicada
Artículo |
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