Strong traces for degenerate parabolic-hyperbolic equations and applications
Young Sam Kwon · Texas ScholarWorks (Texas Digital Library) · 2007
We consider bounded weak solutions u of a degenerate parabolic -hyperbolic equation defined in a subset ]0, T [×Ω ⊂ R + × R d .We define a strong notion of trace at the boundary ]0, T [×∂Ω reached by L 1 convergence for a large class of functionals of u.Such functionals depend on the flux function of the degenerate parabolic-hyperbolic equation and on the boundary.We also prove the well-posedness of the entropy solution for scalar conservation laws with a strong boundary condition with the above trace result as applications.vi