On a class of nonlinear reaction-diffusion systems with nonlocal boundary conditions.
We deal with a class of Penrose-Fife type phase field models for phase transitions, where the phase dynamics is ruled by a Cahn-Hilliard type equation. Suitable assumptions on the behaviour of the heat flux as the absolute temperature tends to zero and to are considered. An existence result is obtained by a double approximation procedure and compactness methods. Moreover, uniqueness and regularity results are proved as well.
2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05We study a singular value problem and the boundary Harnack principle for the fractional Laplacian on the exterior of the unit ball.