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On two types of moving front in quasilinear diffusion
Math. Biosci., 31 (3-4): 307--315 (1976)
Аннотация
Traveling-wave solutions of the equation $u_t=u_xx+f(u)$, when $f$ is convex and nonnegative, have a minimum speed $m^\ast=4f'(0)^1/2$, and this is the speed approached by waves generated by certain physical initial conditions. If $f$ is not convex, $m^\ast$ may exceed $4'f(0)^1/2$; there are qualitative differences in the behavior of such waves. In particular, it is shown that they are more stable, and that time-varying solutions generated by finite initial conditions actually converge uniformly to traveling-wave solutions when $m^\ast>4'f(0)^1/2$.
