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

Garrione, Maurizio;
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.
2019
Saturating diffusion; Fisher-Burgers equation; traveling waves; admissible speeds
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1131144
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