The equivalence of weak solutions and entropy solutions of nonlinear degenerate second-order equations

We prove the equivalence of weak solutions and entropy solutions of an elliptic–parabolic–hyperbolic degenerate equation g(t)t−Δb(u)+div φ(u)=f with homogeneous Dirichlet conditions and initial conditions. As a result of the equivalence, we obtain the L1-contraction principle and uniqueness of weak solutions of elliptic–parabolic degenerate equations.