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A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity. (English) Zbl 1221.35190

Summary: 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.

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35K59 Quasilinear parabolic equations
35K65 Degenerate parabolic equations
45K05 Integro-partial differential equations
80A22 Stefan problems, phase changes, etc.

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References:

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