Uniqueness of renormalized solutions to nonlinear parabolic problems with lower-order terms
Rosaria Di Nardo, Filomena Feo, Olivier Guibé · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2013
We consider a general class of parabolic equations of the type with Dirichlet boundary conditions and with a right-hand side belonging to L1 + Lp′ (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).