A slow pushed front in a Lotka-Volterra competition model
We study the existence and stability of a traveling front in the Lotka-Volterra competition model when the rate of diffusion of one species is small. This front represents the invasion of an unstable homogeneous state by a stable one. It is noteworthy in two respects. First, we show that this front is the selected, or critical, front for this system. We utilize techniques from geometric singular perturbation theory and geometric desingularization. Second, we show that this front appears to be a pushed front in all ways except for the fact that it propagates slower than the linear spreading speed. We show that this is a result of the linear spreading speed arising as a simple pole of the resolvent instead of a branch pole. Using the pointwise Green's function, we show that this pole poses no a priori obstacle to stability of the nonlinear traveling front.