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Fastness and continuous dependence in front propagation in Fisher-KPP equations. (English) Zbl 1154.35380

Summary: We investigate the continuous dependence of the minimal speed of propagation and the profile of the corresponding travelling wave solution of Fisher-type reaction-diffusion equations \[ \vartheta_t = (D(\vartheta)\vartheta_x)_x + f(\vartheta) \] with respect to both the reaction term \(f\) and the diffusivity \(D\). We also introduce and discuss the concept of fast heteroclinic in this context, which allows to interpret the appearance of sharpe heteroclinic in the case of degenerate diffusivity (\(D(0)= 0\)).

MSC:

35K57 Reaction-diffusion equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
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