Uniqueness of renormalized solutions to nonlinear parabolic problems with lower-order terms

Source abstract

We consider a general class of parabolic equations of the type with Dirichlet boundary conditions and with a right-hand side belonging to L 1 + L p′ ( W −1, p ′ ). Using the framework of renormalized solutions we prove uniqueness results under appropriate growth conditions and Lipschitz-type conditions on a(u , ∇ u ), K(u) and H (∇ u ).