Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation
نویسندگان
چکیده
This note investigates the properties of the traveling waves solutions of the nonlocal Fisher equation. The existence of such solutions has been proved recently in [2] but their asymptotic behavior was still unclear. We use here a new numerical approximation of these traveling waves which shows that some traveling waves connect the two homogeneous steady states 0 and 1, which is a striking fact since 0 is dynamically unstable and 1 is unstable in the sense of Turing. Key-words Nonlocal Fisher equation, Turing instability, traveling waves. AMS Subject Classification: 35B36, 92B05, 37M99.
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Rapid traveling waves in the nonlocal Fisher equation connect two unstable states
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