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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Colli, Pierluigi²  Krejci, Pavel³  Rocca, Elisabetta¹  Sprekels, Juergen⁴ 

[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy

[3] Czech Acad Sci, Inst Math, CZ-11567 Prague 1, Czech Republic

[4] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany

关键词: Phase transitions;    Nonlocal models;    Quasilinear integro-differential vectorial equation;   

DOI  :  10.1016/j.jde.2011.02.010

来源: Elsevier

【 摘 要 】

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 chi and on the absolute temperature theta 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free