Abstract
The sign of bistable wave speed indicates the propagation direction of bistable wavefronts. This paper deals with the propagation dynamics of bistable traveling waves for abstract monotone semiflows. We first prove that the bistable wave speed is unique and bounded by spreading speeds of two mono-stable subsystems. We then establish speed-sign determinacy by way of comparison principles. Based on these results, for both irreducible and reducible cases we derive general conditions for determining the speed sign. Finally, the obtained theory is applied to three kinds of evolution systems.
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