The shape of a free boundary driven by a line of fast diffusion

Abstract

We complete the description, initiated in [6], of a free boundary traveling at constant speed in a half plane, where the propagation is controlled by a line having a large diffusion on its own. The main result of this work is that the free boundary is asymptotic to a line at infinity, whose angle to the horizontal is dictated by the velocity of the wave on the line. This helps understanding some counter-intuitive simulations of [7].

Keywords

• free boundary
• travelling wave
• line of fast diffusion