Equivalence of "generalized" solutions for nonlinear parabolic equations with variable exponents and diffuse measure data

. We prove the equivalence of suitably defined weak solutions of a nonhomogeneous initial-boundary value problem for a class of nonlinear parabolic equations. We also develop the notion of both "renormalized" and "entropy" solutions with respect to the "generalized" P(& BULL;)-capacity, initial datum, and diffuse measure data (which does not charge the set of null P(& BULL;)-capacity). Conditions, under which "generalized weak" solutions of the nonhomogeneous problem are in fact well-defined, are also given.