On LeFloch Solutions to Initial-Boundary Value Problem for Scalar Conservation Laws

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• Hélène Frankowska - CNRS and Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie (Paris 6)
• Wednesday 13 April 2011, 13:00-14:00
• Control and Power Seminar Room - EEE Department - level 11.

If you have a question about this talk, please contact Piernicola Bettiol.

We consider an initial-boundary value problem for scalar conservation laws on the strip (0,∞)×[0, 1] with strictly convex smooth flux having a superlinear growth. Such first order partial differential equation is of interest in models of traffic flow. We show that an associated Hamilton-Jacobi equation with initial and (appropriately defined) boundary conditions has a unique generalized solution V that can be obtained as minimum of three value functions of calculus of variations. Each of these functions in turn can be expressed using the Lax formula. Traces of gradients V_x satisfy generalized boundary conditions pointwise when the initial and boundary data are continuous and in a weak sense when they are discontinuous. It is also shown that Vx is continuous almost everywhere and a result concerning traces of sign of f’(V_x(t,·)) is derived.

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