The influence of advection on the propagation phenomena of reaction-diffusion equations with KPP-bistable nonlinearity

This paper is devoted to propagation phenomena for reaction-diffusion-advection equations in one-dimensional heterogeneous environments, where heterogeneity is reflected by the nonlinearity term - being KPP type on ( − ∞ , − L ] (-\infty , -L] and being bistable type on [ L , + ∞ ) [L,+\infty ) for some L > 0 L>0 . A comprehensive analysis is presented on the influence of advection and heterogeneous reactions, based on various values of the advection rate c c . Denote by c m c_m the minimal wave speed of KPP equation and by c b c_b the unique wave speed of bistable equation, respectively. When c > − c m c>-c_m , it is shown that propagation can always occur with leftward spreading speed c m + c c_m+c and rightward spreading speed min ( max ( c b − c , 0 ) , c m − c ) \min \big (\max (c_b-c,0),c_m-c\big ) . Moreover, a logarithmic delay of the level sets in the left direction is discovered. When c ≤