Grim Raindrop: A Translating Solution to Curve Diffusion Flow

2024/12/20 by W. Jacob Ogden, Ogden, W. Jacob, Micah Warren +1 · 1 citation
Environmental Science · Agricultural and Biological Sciences · #Flood Risk Assessment and Management #Soil erosion and sediment transport #Hydrology and Watershed Management Studies

paper · pdf · doi:10.48550/arxiv.2412.15934

Abstract

We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, namely ( (dX)/(dt)) ^⊥=-κ_ssN.

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• Existence of self-similar solutions for the surface diffusion flow with nonlinear boundary conditions in the half space

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