(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
We study the initial-boundary value parabolic problem involving variable exponent under the generalized Leray-Lions conditions. We clarify the definitions of entropy and renormalized solutions to such parabolic problems, and we establish the equivalence between these definitions of entropy and renormalized solutions to the parabolic problems with the Leray-Lions operator and with measure data.