Monotone waves for non-monotone and non-local monostable reaction-diffusion equations (Q281661)

Existence and uniqueness of monotone wavefronts \(u(t,x)=\phi (x+ct)\) are studied for the delayed non-local reaction-diffusion equation NEWLINE\[NEWLINE u_t(t,x)=u_{xx}(t,x)-u(t,x)+\int_R K(x-y) g (u(t-h,y)) dy, u\geq 0,\tag{1}NEWLINE\]NEWLINE where the reaction term \(g\) neither is monotone nor quasi-monotone in some sense.NEWLINENEWLINEThis equation contains as partial cases the non-local KPP-Fisher equation and the delayed diffusive Hutchinson's equation.NEWLINENEWLINEThe main goal of the paper is to provide a new technique allowing to analyze monotonicity of wavefronts for non-monotone and non-local equations (1).