The existence of a renormalized solution of anisotropic parabolic problem for equation with diffuse measure

We consider the first mixed problem for a certain class anisotropic parabolic equations with variable exponents of nonlinearity 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 renormalized solution is proved.