| Abstract: |
| We will discuss some spreading properties of monostable
Lotka- Volterra two-species competition-diffusion
systems when the initial values are null or exponentially decaying in a right
half-line. Thanks to a careful construction of super-solutions
and sub-solutions, we improve previously known results and settle
open questions. In particular, we show that if the weaker competitor
is also the faster one, then it is able to evade
the stronger and slower competitor by invading first into unoccupied territories. The pair of speeds
depends on the initial values. If these are null in a right half-line,
then the first speed is the KPP speed of the fastest competitor and
the second speed is given by an exact formula depending on the first
speed and on the minimal speed of traveling waves connecting the two
semi-extinct equilibria. Furthermore, the unbounded set of pairs of speeds
achievable with exponentially decaying initial values is characterized,
up to a negligible set. |
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