Figure 5 shows that the replicator mobility parameter D acts in an all-or-none manner: zero diffusion kills the system, but almost any positive speed of diffusion is sufficient to maintain coexistence, and further increase in D does not change the results even in the quantitative sense.
if (beta^{2} frac{ 2-alpha) alpha^{3}}{12} < 1), we use the frac{ 2-alpha the proof of Proposition 5.2, Calpha^{3} infer the existence of a traveling wave with positive speed; if (beta^{2} frac{(2-alpha) alpha^{3}}{12} geq1), we find a discontinuous steady state as a consequence of Case 2 in the first part of the proof of Proposition 5.2.
In particular we describe, for different fixed values of γ, the evolution of ignition fronts, characterized by a positive propagation speed, to extinction fronts, characterized by negative speeds, as ϵ is increased.
This is a well known phenomenon for marine vessels moving at positive speed in waves while low-speed applications like dynamic positioning systems are fairly well described with a symmetric system inertia matrix.
Further downstream, reaction overtakes normal diffusion, contributing to a positive displacement speed.
As the front propagates outward, it transitions to an ignition front, and it reaches a positive propagation speed comparable to that of the freely propagating laminar flame.
It is observed that the triple flames maintain a positive displacement speed when the vortex strength is weak, such that they penetrate into the channel between the vortices.
A substantial difference between the polytropic gas and the generalized Chaplygin gas is that the latter has a negative pressure with a positive sound speed.
In any case, it is immediate to see that the existence of a positive admissible speed is possible only if (f u) > 0) in a neighborhood of (u=1).
Then there exists a positive admissible speed for f if and only if the two following conditions simultaneously hold: int_{0}^{1} f u),du > 0 (18) and int_{0}^{1} f^ u),du < 1, (19) where (f^(t)=max{-f(t), 0}).
