Entire solutions for nonlocal dispersal equations with spatio-temporal delay: Monostable case
نویسندگان
چکیده
This paper deals with entire solutions for a general nonlocal dispersal monostable equation with spatiotemporal delay, i.e., solutions that are defined in the whole space and for all time t ∈ R. We first derive a particular model for a single species and show how such systems arise from population biology. Then we construct some new types of entire solutions other than traveling wave solutions and equilibrium solutions of the equation under consideration with quasi-monotone and non-quasi-monotone nonlinearities. Various qualitative properties of the entire solutions are also investigated. In particular, the relationship between the entire solutions and the traveling wave fronts which they originated is considered. Our main arguments are based on the comparison principle, the method of superand sub-solutions, and the construction of auxiliary control systems. © 2014 Elsevier Inc. All rights reserved. MSC: 34K25; 35R10; 92D25
منابع مشابه
Entire Solutions in Bistable Reaction-diffusion Equations with Nonlocal Delayed Nonlinearity
This paper is concerned with entire solutions for bistable reactiondiffusion equations with nonlocal delay in one-dimensional spatial domain. Here the entire solutions are defined in the whole space and for all time t ∈ R. Assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument, we prove the existence of entire solutions whi...
متن کاملTransition fronts and stretching phenomena for a general class of reaction-dispersion equations
We consider a general form of reaction-dispersion equations with non-local dispersal and local reaction. Under some general conditions, we prove the non-existence of transition fronts, as well as some stretching properties at large time for the solutions of the Cauchy problem. These conditions are satisfied in particular when the reaction is monostable and when the dispersal operator is either ...
متن کاملNon-local reaction-diffusion equations with a barrier
Non-local reaction-diffusion equations arise naturally to account for diffusions involving jumps rather than local diffusions related to Brownian motion. In ecology, long distance dispersal require such frameworks. In this work we study a one-dimensional non-local reaction-diffusion equation with bistable and monostable type reactions. The heterogeneity here from due to the presence of a barrie...
متن کاملTraveling Fronts in Monostable Equations with Nonlocal Delayed Effects
In this paper, we study the existence, uniqueness and stability of traveling wave fronts in the following nonlocal reaction–diffusion equation with delay ∂u (x, t) ∂t = d u (x, t)+ f ⎛ ⎝u (x, t) , ∞ ∫ −∞ h (x − y) u (y, t − τ) dy ⎞ ⎠. Under the monostable assumption, we show that there exists a minimal wave speed c∗ > 0, such that the equation has no traveling wave front for 0 < c < c∗ and a tr...
متن کاملExistence of Entire Solutions for Non-local Delayed Lattice Differential Equations
In this article we study entire solutions for a non-local delayed lattice differential equation with monostable nonlinearity. First, based on a concavity assumption of the birth function, we establish a comparison theorem. Then, applying the comparison theorem, we show the existence and some qualitative features of entire solutions by mixing a finite number of traveling wave fronts with a spati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015