Entire solutions of nonlocal dispersal equations with monostable nonlinearity in space periodic habitats
نویسندگان
چکیده
منابع مشابه
Entire solutions for nonlocal dispersal equations with spatio-temporal delay: Monostable case
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 ...
متن کاملNon-local Anisotropic Dispersal with Monostable Nonlinearity
We study the travelling wave problem J ⋆ u− u− cu + f(u) = 0 in R, u(−∞) = 0, u(+∞) = 1 with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for c 6= 0. For c = 0 we show examples of non-uniqueness.
متن کاملEntire 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 کاملExistence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity
Let J ∈ C(R), J ≥ 0, R J = 1 and consider the nonlocal diffusion operator M[u] = J ? u− u. We study the equation Mu + f(x, u) = 0, u ≥ 0 in R, where f is a KPP type non-linearity, periodic in x. We show that the principal eigenvalue of the linearization around zero is well defined and a that a nontrivial solution of the nonlinear problem exists if and only if this eigenvalue is negative. We pro...
متن کاملPlanar Traveling Waves for Nonlocal Dispersion Equation with Monostable Nonlinearity
In this paper, we study a class of nonlocal dispersion equation with monostable nonlinearity in n-dimensional space ut − J ∗ u+ u+ d(u(t, x)) = ∫ Rn fβ(y)b(u(t− τ, x− y))dy, u(s, x) = u0(s, x), s ∈ [−τ, 0], x ∈ Rn, where the nonlinear functions d(u) and b(u) possess the monostable characters like Fisher-KPP type, fβ(x) is the heat kernel, and the kernel J(x) satisfies Ĵ(ξ) = 1 − K|ξ|α + o(|ξ|...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2016
ISSN: 0022-0396
DOI: 10.1016/j.jde.2016.05.006