Vasseur, Alexis F.1736103412008-08-282017-05-112008-08-282017-05-112007-05http://hdl.handle.net/2152/3166textWe consider bounded weak solutions u of a degenerate parabolic-hyperbolic equation defined in a subset [mathematical symbols]. We define strong notion of trace at the boundary [mathematical symbols] reached by L¹ 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.electronicengCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.Differential equations, Hyperbolic--Numerical solutionsDifferential equations, Parabolic--Numerical solutionsDegenerate differential equationsCauchy problem--Numerical solutionsThesis