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Dynamics, Geometry and Groups Seminar

Speaker: Maria Teresa Chiri (¾ÅÐãÖ±²¥)

Title: Conservation laws with flux discontinuous in the conserved quantity

Abstract:
We investigate a class of conservation laws where the flux function is discontinuous with respect to the conserved quantity, motivated by applications such as conveyor belt systems and traffic flow models. This discontinuity gives rise to solutions associated with multivalued fluxes, which we interpret as pairs consisting of a conserved quantity and its corresponding flux. These solutions can be obtained as limits of conservation laws with regularized fluxes, whose approximations exhibit shocks with arbitrarily large slopes. As a consequence, the fundamental property of finite speed of propagation no longer holds, and information may propagate instantaneously. In this talk, we introduce a suitable notion of entropy solution for the associated boundary value problem, establish existence via front-tracking techniques, and prove Kruzhkov-type stability estimates.