BOUNDARY SINGULARITY ANALYSIS FOR A CLASS OF QUASILINEAR DEGENERATE PARABOLIC SYSTEMS WITH MIXED CONSTRAINTS

Abstract

This paper investigates the local regularity and bound ary singularity behavior of solutions to a specific class of quasilinear degenerate parabolic systems. Our investigation focuses on the critical dynamics at the interface of mixed boundary constraints, where the transition between Dirichlet and Neumann conditions induces analytical discontinuities. By implementing a localized analysis and utilizing capacity based geometric criteria, we establish sufficient conditions for the removability of boundary singularities in non smooth domains. In contrast to traditional global energy methods, we adapt De Giorgi-Nash-Moser techniques to analyze the solution behavior near the singular set. By establishing a rigorous linkage between the capacity density of the boundary and the local mea
sure of the level sets, we demonstrate that Hölder continuity is preserved under specific geometric constraints. These results provide a consistent analytical framework for understanding the stability of degenerate diffusion systems in the presence of complex boundary interfaces, with direct implications for non-Newtonian flow models
in heterogeneous media