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The inviscid limit of viscous Burgers at nondegenerate shock formation
Sanchit Chaturvedi, Cole Graham
We study the vanishing viscosity limit of the one-dimensional Burgers equation near nondegenerate shock formation. We develop a matched asymptotic expansion that describes small-vi…
The distance between the two BBM leaders
Julien Berestycki, Éric Brunet, Cole Graham +3
We study the distance between the two rightmost particles in branching Brownian motion. Derrida and the second author have shown that the long-time limit of this random va…
Reaction-diffusion equations in the half-space
Henri Berestycki, Cole Graham
We study reaction-diffusion equations of various types in the half-space. For bistable reactions with Dirichlet boundary conditions, we prove conditional uniqueness: there is a uni…
The Bramson correction for Fisher--KPP equations with nonlocal diffusion
Cole Graham
We establish the logarithmic Bramson correction to the position of solutions to the Fisher--KPP equation with nonlocal diffusion. Solutions with step-like initial data typically re…
Precise asymptotics for Fisher-KPP fronts
Cole Graham
We consider the one-dimensional Fisher-KPP equation with step-like initial data. Nolen, Roquejoffre, and Ryzhik showed that the solution converges at long time to a traveling w…