The Lighthill acoustic analogy, as embodied in the Ffowcs Williams{Hawkings (FW{H) equation, is compared with the Kirchho formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchho advantage (namely nonlinear ow e ects are included in the surface integration) is also available to the FW{H method if the integration surface used in the FW{H equation...

The Whitham equation was proposed as a model for surface water waves that combines the quadratic flux nonlinearity $f(u) = \tfrac{1}{2}u^2$ of Korteweg-de Vries and full linear dispersion relation $\Omega(k) \sqrt{k\tanh k}$ uni-directional gravity in suitably scaled variables. This paper proposes analyzes generalization Whitham's to unidirectional nonlinear wave equations consisting general fu...

The Korteweg-de Vries (KdV) equation is widely recognized as a simple model for unidirectional weakly nonlinear dispersive waves on the surface of a shallow body of fluid. While solutions of the KdV equation describe the shape of the free surface, information about the underlying fluid flow is encoded into the derivation of the equation, and the present article focuses on the formulation of mas...

We investigate a class of hybrid systems driven by partial differential equations for which the infinite dimensional state can switch in time and in space at the same time. We consider a particular class of such problems (switched Hamilton-Jacobi equations) and define hybrid components as building blocks of hybrid solutions to such problems, using viability theory. We derive sufficient conditio...

For a convex conservation law ut + f(u)x = 0, u(x, 0) = u0(x), −∞ < x <∞, t > 0, bounded initial data u0(x), are considered that take on constant values u− to the left of a bounded interval, and u+ to the right, with u− > u+. The solution of the initial value problem is shown to collapse in finite time to a single shock wave joining u− to u+. The proof involves comparison with a solution having...

We consider an Enskog-like discrete velocity model which in the limit yields the viscous Lighthill-Whitham-Richards equation used to describe vehicular traffic flow. Consideration is given to a discrete velocity model with two speeds. Extensions to the Aw-Rascle system and more general discrete velocity models are also discussed. In particular, only positive speeds are allowed in the discrete v...

On the basis of the elementary laws of individual driver behavior concerning the acceleration and interaction of vehicles a gas-kinetic traffic model is constructed. This yields theoretical relations for the fundamental diagram and the equilibrium variance-density relation, but above all it allows the derivation of macroscopic traffic equations. These build a hierarchy of non-closed equations w...