Strong traces for degenerate parabolic-hyperbolic equations
Young‐Sam Kwon · Discrete and Continuous Dynamical Systems · 2009
In this paper we consider bounded weak solutions $u$ of degenerateparabolic-hyperbolic equations defined in a subset$]0,T[\times\Omega\subset \R^{+}\times \R^d$. We define a strongnotion of trace at the boundary $]0,T[\times\partial\Omega$ reachedby $L^1$ convergence for a large class of functionals of $u$ and at$0 \times \Omega$ reached by $L^1$ convergence for solution $u$.This result develops the strong trace results of Kwon, Vasseur[13] and Panov [19, 20] for more generalequations, namely, degenerate parabolic-hyperbolic equations.