A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity

0360085 - MÚ 2012 RIV US eng J - Článek v odborném periodiku
Colli, P. - Krejčí, Pavel - Rocca, E. - Sprekels, J.
A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity.
Journal of Differential Equations. Roč. 251, 4-5 (2011), s. 1354-1387. ISSN 0022-0396. E-ISSN 1090-2732
Grant CEP: GA ČR GAP201/10/2315
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: phase transitions * nonlocal models * quasilinear integro-differential vectorial equation
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.277, rok: 2011
http://www.sciencedirect.com/science/article/pii/S0022039611000775

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.
Trvalý link: http://hdl.handle.net/11104/0197721