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A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity
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SYSNO ASEP 0360085 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity Author(s) Colli, P. (IT)
Krejčí, Pavel (MU-W) RID, SAI, ORCID
Rocca, E. (IT)
Sprekels, J. (DE)Source Title Journal of Differential Equations. - : Elsevier - ISSN 0022-0396
Roč. 251, 4-5 (2011), s. 1354-1387Number of pages 34 s. Language eng - English Country US - United States Keywords phase transitions ; nonlocal models ; quasilinear integro-differential vectorial equation Subject RIV BA - General Mathematics R&D Projects GAP201/10/2315 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000291900800024 EID SCOPUS 79958191500 DOI 10.1016/j.jde.2011.02.010 Annotation In this paper, we prove the existence and global boundedness from above for a solution to an integro-differential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a quasilinear internal energy balance ruling the evolution of the absolute temperature with a vectorial integro-differential inclusion governing the (vectorial) phase-parameter dynamics. The specific heat and the heat conductivity k are allowed to depend both on the order parameter χ and on the absolute temperature θ of the system, and the convex component of the free energy may or may not be singular. Uniqueness and continuous data dependence are also proved under additional assumptions. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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