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Large Convection Limits for KPP Fronts
This paper is concerned with the KPP equation with strong convection. The asymptotic behavior of the minimal speed of traveling fronts is derived for shear flow convection and for cellular flow convection. In the first case a new limit problem is derived and analyzed. For cellular flows new almost optimal upper bounds are obtained in terms of the wave speed of the homogenized problem. Thereby some conjectures on the asymptotic growth of front speeds are confirmed.