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An existence result for a hyperbolic phase transition problem with memory
No full textAbstractIn this note we deal with a phase transition model based on the Gurtin-Pipkin approach for the heat conduction in materials with memory and accounting for dynamical supercooling and superheating effects. The constitutive laws and the balance law of (linearized) energy, supplied with suitable initial and boundary conditions, yield an evolution problem coupling a hyperbolic equation for the temperature with a variational inequality for the phase variable. The existence of a weak solution is proved by passing to the limit in an approximating problem withthe help of monotonicity and compactness techniques
Regularity results for a Cahn-Hilliard-Navier-Stokes system with shear dependent viscosity
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