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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)

- Chun-Chi Lin, Hartmut R. Schwetlick
- SIAM Journal of Applied Mathematics
- 2004

Recently, rod theory has been applied to the mathematical modeling 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)

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

In this paper, we evolve hypersurfaces represented as graphs of strictly convex functions over strictly convex bounded domains by the non-parametric logarithmic Gauß curvature flow subject to a Neumann boundary condition. We show that solutions exist for all time and converge smoothly to translating solutions. To be more precise, we address the following… (More)

- Oliver C. Schnürer, Hartmut R. Schwetlick, OLIVER C. SCHNÜRER, Hartmut R. Schwetlick
- 2005

We consider solutions to linear parabolic equations with initial data decaying at spatial infinity. For a class of advection-diffusion equations with a spatially dependent velocity field, we study the behavior of solutions as time tends to infinity. We characterize velocity fields, so that positive solutions decay or lift-off at spatial infinity as time… (More)

We consider a nonlinear transport equation as a hyperbolic generalisation of the well-known reaction diffusion equation. Themodel 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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