L1-contraction and uniqueness for quasilinear elliptic-parabolic equations

Abstract

We prove the L1-contraction principle and uniqueness of solutions for quasilinear elliptic-parabolic equations of the form ∂t[b(u)] - div[a(∇u, b(u))] + f(b(u)) = 0 in (0, T) × Ω, where b is monotone nondecreasing and continuous. We assume only that u is a weak solution of finite energy. In particular, we do not suppose that the distributional derivative ∂t[b(u)] is a bounded Borel measure or a locally integrable function. © 1996 Academic Press, Inc.