| Abstract: |
| This talk is concerned with reaction-diffusion-advection equations in homogeneous or spatially periodic media. I will discuss the asymptotic properties of the solutions of the Cauchy problem, under an assumption of weak stability of the constant steady states 0 and 1, or for Fisher-KPP reactions. I will especially show that front profiles appear, along sequences of times and points, in the large-time dynamics of the solutions, whether their initial supports be bounded or unbounded. I will also discuss further geometrical properties of the asymptotic invasion shapes of invading solutions. The talk is based on some joint works with Hongjun Guo and Luca Rossi. |
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