We propose a new approach for proving existence of monotone wavefronts in non-monotone and non local monostable diffusive equations. This allows to extend recent results established for the particular case of equations ...

We are revisiting the topic of travelling fronts for the food-limited (FL) model with spatio-temporal nonlocal reaction. These solutions are crucial for understanding the whole model dynamics. Firstly, we prove the existence ...

Copyright © Royal Society of Edinburgh 2019.We are revisiting the topic of travelling fronts for the food-limited (FL) model with spatio-temporal nonlocal reaction. These solutions are crucial for understanding the whole ...

We study the wavefront solutions of the scalar reaction-diffusion equations ut(t, x) = Δu(t, x)-u(t, x)+g(u(t-h,x)), with monotone reaction term g : ℝ+ → ℝ+ and h > 0. We are mostly interested in the situation when the ...

We consider the nonlocal KPP-Fisher equation u(t)(t, x) = u(xx)(t, x) u(t, x)(1 - (K * u)(t, x)) which describes the evolution of population density u(t, x) with respect to time t and location x. The non-locality is expressed ...

We study the asymptotic stability of traveling fronts and the front's velocity selection problem for the time-delayed monostable equation with Lipschitz continuous reaction term . We also assume that g is -smooth in some ...