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We consider the Fisher-KPP equation with a non-local interaction term. Weestablish a condition on the interaction that allows for existence ofnon-constant periodic solutions, and prove uniform upper bounds for thesolutions of the Cauchy problem, as well as upper and lower bounds on thespreading rate of the solutions with compactly supported initial data.

On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds