Conservation laws with singular nonlocal sources

Well-Posedness of Scalar Conservation Laws with Singular Sources

We consider scalar conservation laws with nonlinear singular sources with a concentration effect at the origin. We assume that the flux A is not degenerated and we study whether it is possible to define a well-posed limit problem. We prove that when A is strictly monotonic then the limit problem is well-defined and has a unique solution. The definition of this limit problem involves a layer whi...

Nonlocal symmetries and nonlocal conservation laws of Maxwell’s equations

Nonlocal symmetries are obtained for Maxwell’s equations in three space–time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the co...

Nonlocal conservation laws for supersymmetric KdV equations

The nonlocal conservation laws for the N=1 supersymmetric KdV equation are shown to be related in a simple way to powers of the fourth root of its Lax operator. This provides a direct link between the supersymmetry invariance and the existence of nonlocal conservation laws. It is also shown that nonlocal conservation laws exist for the two integrable N=2 supersymmetric KdV equations whose recur...

Conservation laws with a nonlocal flow, Application to pedestrian traffic

Viscous System of Conservation Laws: Singular Limits

Abstract. We continue our analysis of the Cauchy problem for viscous system of conservation, under natural assumptions. We examine in which way does the existence time depend upon the viscous tensor B(u). In particular, we consider singular limits, where the rank of the symbol B(u; ξ) drops at the limit. This covers a lot of situations, for instance that of the limit of the Navier-Stokes-Fourie...