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Abstract. This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the vanishing viscosity method and finite difference schemes (Lax-Friedrichs type schemes, Godunov scheme). We demonstrate that different regularization methods generate different boundary layers. Hence, the boundary condition can be formulated only if an approximation scheme is selected first. Assuming solely uniform L ∞ bounds on the approximate solutions and so dealing with L ∞ solutions, we derive several entropy inequalities satisfied by the boundary layer in each case under consideration. A Young measure is introduced to describe the boundary trace. When a uniform bound on the total variation is available, the boundary Young measure reduces to a Dirac mass. Form the above analysis, we deduce several formulations for the boundary condition which apply whether the boundary is characteristic or not. Each formulation is based a set of admissible boundary values, following Dubois and LeFloch's terminology in "Boundary conditions for nonlinear hyperbolic systems of conservation laws", J. Diff. Equa. 71 (1988), 93-122. The local structure of those sets and the well-posedness of the corresponding initial-boundary value problem are investigated. The results are illustrated with convex and nonconvex conservation laws and examples from continuum mechanics.

SummaryThe influence of honey on collagen metabolism during wound healing was assessed by making an excision wound by cutting away a 4 cm2 full thickness piece of skin from the shaven back of rats under ether anaesthesia. One milliliter of pure, commercial, unboiled honey was applied topically or administered systemically. The rate of collagen synthesis was assessed by administration of [3H]proline, 24 h before sacrifice of the animals. The granulation tissues formed were removed and used to study the various fractions of collagen, susceptibility of collagen to denaturing agents, and the aldehyde content of collagen. The results show that honey accelerates wound healing when applied topically or administered systemically but that systemic treatment is more effective than the topical application.

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