A Priori Estimates and Regularity of Solutions to Nonlinear Parabolic Equations in Generalized Morrey Spaces

ABSTRACT In this paper, we derive generalized Morrey space estimates for the gradient of weak solutions associated with nonlinear parabolic equations in non‐smooth domains. Regarding the nonlinearity, we assume it is measurable with respect to the time variable , while exhibiting small BMO characteristics with respect to the spatial variable . In addition, we present a numerical application that models the time‐dependent propagation of heat or pressure in a subsurface environment using a parabolic PDE and the Crank‐Nicolson method, supporting our theoretical findings with visual simulations.