Asymptotic behavior of traveling fronts and entire solutions for a nonlocal monostable equation

2010 ◽  
Vol 72 (9-10) ◽  
pp. 3659-3668 ◽  
Author(s):  
Guangying Lv
Keyword(s):  
Asymptotic Behavior ◽  
Entire Solutions ◽  
Traveling Fronts ◽  
Monostable Equation

Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations

2020 ◽  
Vol 20 (4) ◽  
pp. 769-781
Author(s):  
Limei Dai ◽  
Jiguang Bao
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Entire Solutions ◽  
Perron Method ◽  
The Cauchy Problem ◽  
Monge Ampere

AbstractIn this paper, we study the Cauchy problem of the parabolic Monge–Ampère equation-u_{t}\det D^{2}u=f(x,t)and obtain the existence and uniqueness of viscosity solutions with asymptotic behavior by using the Perron method.

scholarly journals Entire solution originating from three fronts for a discrete diffusive equation

2017 ◽  
Vol 48 (2) ◽  
pp. 215-226 ◽  
Author(s):  
Yan Yu Chen
Keyword(s):  
Entire Solution ◽  
Entire Solutions ◽  
Traveling Fronts ◽  
Bistable Nonlinearity

In this paper, we study a discrete diffusive equation with a bistable nonlinearity. For this equation, there are three types of traveling fronts. By constructing some suitable pairs of super-sub-solutions, we show that there are only two types of entire solutions originating from three fronts of this equation. These results show us some new dynamics of this discrete diffusive equation.

Radial Symmetry of Entire Solutions of a Biharmonic Equation with Supercritical Exponent

2019 ◽  
Vol 19 (2) ◽  
pp. 291-316
Author(s):  
Zongming Guo ◽  
Long Wei
Keyword(s):  
Asymptotic Behavior ◽  
Biharmonic Equation ◽  
Sufficient Conditions ◽  
Entire Solution ◽  
Radial Symmetry ◽  
Entire Solutions ◽  
Moving Plane ◽  
Exact Asymptotic Behavior ◽  
Necessary And Sufficient ◽  
Positive Entire Solution

AbstractNecessary and sufficient conditions for a regular positive entire solution u of a biharmonic equation\Delta^{2}u=u^{p}\quad\text{in }\mathbb{R}^{N},\,N\geq 5,\,p>\frac{N+4}{N-4}to be a radially symmetric solution are obtained via the exact asymptotic behavior of u at {\infty} and the moving plane method (MPM). It is known that above equation admits a unique positive radial entire solution {u(x)=u(|x|)} for any given {u(0)>0}, and the asymptotic behavior of {u(|x|)} at {\infty} is also known. We will see that the behavior similar to that of a radial entire solution of above equation at {\infty}, in turn, determines the radial symmetry of a general positive entire solution {u(x)} of the equation. To make the procedure of the MPM work, the precise asymptotic behavior of u at {\infty} is obtained.

On the Existence of Positive Decaying Entire Solutions for a Class of Sublinear Elliptic Equations

1988 ◽  
Vol 40 (5) ◽  
pp. 1156-1173 ◽  
Author(s):  
Yasuhiro Furusho ◽  
Takaŝi Kusano
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic Equations ◽  
Early Stage ◽  
Nonlinear Elliptic Equations ◽  
Entire Solution ◽  
Entire Solutions ◽  
Nonlinear Elliptic ◽  
The Subject ◽  
Image Position ◽  
Simple Equations

In recent years there has been a growing interest in the existence and asymptotic behavior of entire solutions for second order nonlinear elliptic equations. By an entire solution we mean a solution of the elliptic equation under consideration which is guaranteed to exist in the whole Euclidean N-space RN, N ≧ 2. For standard results on the subject the reader is referred to the papers [2-7, 9-21].The study of entire solutions, which at an early stage was restricted to simple equations of the form Δu + f(x, u) = 0, x ∊ RN, Δ being the N-dimensional Laplacian, has now been extended and generalized to elliptic equations of the typeAwhere

Sign in / Sign up

Export Citation Format

Share Document