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We consider a nonlinear transport equation as a hyperbolic generalisation of the well-known reaction diiusion equation. We show the existence of strictly monotone travelling fronts for the three main types of the nonlinearity: the positive source term, the combustion law, and the bistable case. In the rst case there is a whole interval of possible speeds… (More)

- Oliver C. Schnürer, Hartmut R. Schwetlick, HARTMUT R. SCHWETLICK
- 2003

We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauß curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In particular, for bounded domains we prove that convex functions with prescribed normal derivative satisfy a uniform… (More)

Recently, rod theory has been applied to the mathematical model-ing of bacterial fibers and biopolymers (e.g. DNA), to study their mechanical properties and shapes (e.g. supercoiling). In static rod theory, an elastic rod in equilibrium is the critical point of an elastic energy. This induces a natural question of how to find elasticae. In this paper, we… (More)

L 2-flow of elastic curves with knot points and clamped ends Abstract. In this paper we investigate the L 2-flow of elastic non-closed curves in n-dimensional Euclidean spaces with knot points and two clamped ends. The L 2-flow corresponds to a fourth-order parabolic equation on each piece of curve between two successive knot points with certain dynamic… (More)

We consider a nonlinear transport equation as a hyperbolic gen-eralisation of the well-known reaction diffusion equation. The model is based on earlier work of K.P. Hadeler attempting to include run-and-tumble motion into the mathematical description. Previously, we proved the existence of strictly monotone travelling fronts for the three main types of the… (More)

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