A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity
Authors
- Colli, Pierluigi
ORCID: 0000-0002-7921-5041 - Krejčí, Pavel
ORCID: 0000-0002-7579-6002 - Rocca, Elisabetta
ORCID: 0000-0002-9930-907X - Sprekels, Jürgen
ORCID: 0009-0000-0618-8604
2010 Mathematics Subject Classification
- 35K51 35K59 35K65 45K05 80A22
Keywords
- Phase transitions, nonlocal, models, quasilinear, integrodifferential vectorial, equation
DOI
Abstract
In this paper, we prove the existence and global boundedness from above for a solution to an integrodifferential 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.
Appeared in
- J. Differential Equations, 251 (2011) pp. 1354--1387.
Download Documents