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On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds (1307.3001v1)
Published 11 Jul 2013 in math.AP
Abstract: 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.