388 research outputs found
On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds
We consider the Fisher-KPP equation with a non-local interaction term. We
establish a condition on the interaction that allows for existence of
non-constant periodic solutions, and prove uniform upper bounds for the
solutions of the Cauchy problem, as well as upper and lower bounds on the
spreading rate of the solutions with compactly supported initial data
The stochastic acceleration problem in two dimensions
We consider the motion of a particle in a two-dimensional spatially
homogeneous mixing potential and show that its momentum converges to the
Brownian motion on a circle. This complements the limit theorem of Kesten and
Papanicolaou \cite{KP} proved in dimensions
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