Concept

Curve-shortening flow

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A vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

Curve-shortening flow

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Robustness via curvature regularization, and vice versa

A vector field method on the distorted Fourier side and decay for wave equations with potentials

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Directed mean curvature flow in noisy environment

Effects of aquifer geometry on seawater intrusion in annulus segment island aquifers

Robustness via curvature regularization, and vice versa

Isogeometric Analysis of geometric partial differential equations

An experimental study on main flow, secondary flow and turbulence in open-channel bends with emphasis on their interaction with the outer-bank geometry

Meander dynamics: A nonlinear model without curvature restrictions for flow in open-channel bends

Processes governing the flow redistribution in sharp river bends

Robustness via curvature regularization, and vice versa

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

A vector field method on the distorted Fourier side and decay for wave equations with potentials