Klaus Dressler

A kinetic method for strictly nonlinear conservation laws

Ideas from kinetic theory are used to construct a new solution method for nonlinear conservation laws of the formu1+f(u)x=0. We choose a class of distribution functionsG=G(t, x, ξ), which are compactly supported with respect to the artificial velocityξ. This can be done in an optimal way, i.e. so that theξ-integral of the solution of the linear kinetic equationGt+ξGx=0 solves the nonlinear conservation law exactly.Introducing a time step and variousx-discretisations one easily obtains a variety of numerical schemes. Among them are interesting new methods as well as known upstream schemes, which get a new interpretation and the possibility to incorporate boundary value problems this way.

Notes on Lipschitz estimates for the stop and play operator in plasticity

We present a generalisation of existing Lipschitz estimates for the stop and play operator for an arbitrary convex and closed characteristic, which contains the origin, in a separable Hilbert space. We are especially concerned with the dependence of stop and play on different scalar products.