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We establish a new property of Fisher-KPP type propagation in a plane, in thepresence of a line with fast diffusion. We prove that the line enhances theasymptotic speed of propagation in a cone of directions. Past the criticalangle given by this cone, the asymptotic speed of propagation coincides withthe classical Fisher-KPP invasion speed. Several qualitative properties arefurther derived, such as the limiting behaviour when the diffusion on the linegoes to infinity.

The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations