This paper deals with the existence of monotone heteroclinic traveling waves for some reaction-convection-diffusion equations with saturating (and possibly density-dependent) nonlinear diffusion, modeling physical situations where a saturation effect appears for large values of the gradient. An estimate for the critical speed—namely, the least speed for which a monotone heteroclinic traveling wave exists—is provided in the presence of different kinds of reaction terms (e.g., monostable and bistable ones). The dependence of the admissible speeds on a small real parameter breaking the diffusion is also briefly discussed, and some numerical simulations are also shown.
Heteroclinic traveling fronts for reaction-convection-diffusion equations with a saturating diffusive term
Strani M.
2019-01-01
Abstract
This paper deals with the existence of monotone heteroclinic traveling waves for some reaction-convection-diffusion equations with saturating (and possibly density-dependent) nonlinear diffusion, modeling physical situations where a saturation effect appears for large values of the gradient. An estimate for the critical speed—namely, the least speed for which a monotone heteroclinic traveling wave exists—is provided in the presence of different kinds of reaction terms (e.g., monostable and bistable ones). The dependence of the admissible speeds on a small real parameter breaking the diffusion is also briefly discussed, and some numerical simulations are also shown.I documenti in ARCA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.