Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations
نویسندگان
چکیده
Assume a single reaction-diffusion equation has zero as an asymptotically stable stationary point. Then we prove that there exist no localized travelling waves with non-zero speed. That is, if [lim inf |x|→∞ u(x), lim sup|x|→∞ u(x)] is included in an open interval of zero that does not include other stationary points, then the speed has to be zero or the travelling profile u has to be identically zero. 2010 Mathematics Subject Classification: 35C07, 35K57
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