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Strong traces for degenerate parabolic-hyperbolic equations
In this paper we consider bounded weak solutions $u$ of degenerate
parabolic-hyperbolic equations defined in a subset
$]0,T[\times\Omega\subset \R^{+}\times \R^d$. We define a strong
notion of trace at the boundary $]0,T[\times\partial\Omega$ reached
by $L^1$ 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 general
equations, namely, degenerate parabolic-hyperbolic equations.