| Abstract: |
| In this talk, we present some recent results obtained in collaboration with M. Alfaro and L. Du regarding the propagation in non-local Fisher-KPP equations with asymmetric convolution kernels. Our focus is on kernels that depend on a given norm, and we address the following natural geometric question: does the asymptotic invasion shape coincide with the ball corresponding to that norm? Contrary to what one might expect, the answer is generally negative. In fact, the shape of the invasion set (and not just its size) is the result of a non-trivial interplay between the kernel and the reaction term. The geodesic ball is only obtained in the limit as the reaction term tends to infinity. The arguments rely on a careful analysis of the regularity and geometric properties of the Wulff shape provided by the Freidlin-Gartner formula. |
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