A Qualitative Analysis of a Nonlinear Second-Order Anisotropic Diffusion Problem with Non-homogeneous Cauchy–Stefan–Boltzmann Boundary Conditions

Abstract

The paper is concerned with a qualitative analysis for a nonlinear second-order parabolic problem, subject to non-homogeneous Cauchy–Stefan–Boltzmann boundary conditions, extending the types already studied. Under certain assumptions, we prove the existence, a priori estimates, regularity and uniqueness of a solution in the class $$W^{1,2}_p(Q)$$. Here we extend the results already proven by the authors for a nonlinearity of cubic type, making the present mathematical model to be more capable for describing the complexity of certain wide classes of real physical phenomena (phase separation and transition, for instance).