Ohio University
Athens, Ohio, U. S. A.
A non-Fourier phase field model, which is described by a system of integro-partial differential equations, is considered. The existence, regularity, and asymptotic properties of solutions to that system are discussed. The approach relies on a combination of monotonicity methods and fixed point techniques, as well as on the theory of abstract linear Volterra equations with positive kernels. A related degenerate nonlinear Volterra equation, which arises in the study of Stefan problems and Hele-Shaw flows in materials with memory, will also be analyzed.