Existence of a Renormalized Solution to an Anisotropic Parabolic Problem for an Equation with Diffuse Measure

The first initial–boundary value problem is considered for a class of anisotropic parabolic equations with variable nonlinearity exponents and a diffuse measure on the right-hand side in a cylindrical domain $(0,T)\times \Omega $. The domain $\Omega $ is bounded. The existence of a renormalized solution is proved.