Global Well-posedness Result for Nonlinear Unilateral Parabolic Equations in Musielak Spaces

This study investigates the existence and uniqueness of solutions for a class of nonlinear parabolic equations characterized by integrable data within time-dependent Musielak-Orlicz spaces. By employing density arguments and advanced variational techniques, we demonstrate the existence of entropy solutions. The framework developed herein is robust enough to encompass various mathematical models, including those involving double-phase growth, variable exponents, and Orlicz-type growth conditions.