A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity
Please always quote using this URN:urn:nbn:de:0296-matheon-10685
- 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 $\teta$ 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.