EXISTENCE AND UNIQUENESS OF RENORMALIZED SOLUTIONS TO PARABOLIC PROBLEMS FOR EQUATIONS WITH DIFFUSE MEASURE

摘要

We consider the first mixed problem for anisotropic parabolic equations with variable nonlinearity exponents and diffuse measure on the right-hand side in the cylindrical domain (0, T) × Ω, where Ω is a bounded domain. We establish the existence of a renormalized solution. The uniqueness of the renormalized solution is proved under the assumption that the functions entering the equation are locally Lipschitz.