For vector-valued Allen-Cahn gradient flows with a bounded lower-energy region, there exists a traveling wave with a unique largest speed, obtained as the zero of a variational energy.
Chen,Existence, uniqueness, and asymptotic stability of travelling waves in non-local evolution equa- tions, Adv
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Existence of traveling waves for vector valued gradient flows
For vector-valued Allen-Cahn gradient flows with a bounded lower-energy region, there exists a traveling wave with a unique largest speed, obtained as the zero of a variational energy.