EFFECT OF CROSS DIFFUSION IN A COMPETITION MODEL WITH STAGE STRUCTURE

2012 ◽  
Vol 05 (06) ◽  
pp. 1250052 ◽  
Author(s):  
LINA ZHANG ◽  
SHENGMAO FU ◽  
PING HU
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Stage Structure ◽  
Competition Model ◽  
Positive Equilibrium ◽  
Cross Diffusion ◽  
Homogeneous Neumann Boundary Condition

The purpose of this paper is to study the effect of cross diffusion in a competition model with stage structure, under homogeneous Neumann boundary condition. It will be shown that cross diffusion cannot only destabilize a uniform positive equilibrium, it can also help diffusion to induce instability of the uniform positive equilibrium. Moreover, stationary patterns can arise from the effect of cross diffusion.

Dynamics Analysis in a Gierer–Meinhardt Reaction–Diffusion Model with Homogeneous Neumann Boundary Condition

2019 ◽  
Vol 29 (09) ◽  
pp. 1930025 ◽  
Author(s):  
Xiang-Ping Yan ◽  
Ya-Jun Ding ◽  
Cun-Hua Zhang
Keyword(s):  
Boundary Condition ◽  
Hopf Bifurcation ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Reaction Diffusion Equations ◽  
Positive Equilibrium ◽  
Reaction Diffusion Model ◽  
Homogeneous Neumann Boundary Condition

A reaction–diffusion Gierer–Meinhardt system with homogeneous Neumann boundary condition on one-dimensional bounded spatial domain is considered in the present article. Local asymptotic stability, Turing instability and existence of Hopf bifurcation of the constant positive equilibrium are explored by analyzing in detail the associated eigenvalue problem. Moreover, properties of spatially homogeneous Hopf bifurcation are carried out by employing the normal form method and the center manifold technique for reaction–diffusion equations. Finally, numerical simulations are also provided in order to check the obtained theoretical conclusions.

Positive steady states of the Holling–Tanner prey–predator model with diffusion

2005 ◽  
Vol 135 (1) ◽  
pp. 149-164 ◽  
Author(s):  
Rui Peng ◽  
Mingxin Wang
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Steady States ◽  
Homogeneous Neumann Boundary Condition ◽  
Positive Steady States ◽  
Predator Model

This paper is concerned with the Holling–Tanner prey–predator model with diffusion subject to the homogeneous Neumann boundary condition. We obtain the existence and non-existence of positive non-constant steady states.

Asymptotics of solutions to a convection—diffusion equation on the half-line

2000 ◽  
Vol 130 (4) ◽  
pp. 837-853 ◽  
Author(s):  
G. Karch
Keyword(s):  
Boundary Condition ◽  
Asymptotic Expansion ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Half Line ◽  
Asymptotics Of Solutions ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Homogeneous Neumann Boundary Condition ◽  
Higher Order Terms

We study the behaviour, as t → ∞, of solutions to the convectiondiffusion equation on the half-line with the homogeneous Neumann boundary condition and with bounded initial data. The higher-order terms of the asymptotic expansion in Lp (R+) of solutions are derived.

On the set of eigenvalues of some PDEs with homogeneous Neumann boundary condition

2015 ◽  
Vol 116 ◽  
pp. 19-25 ◽  
Author(s):  
Maria Fărcăşeanu ◽  
Mihai Mihăilescu ◽  
Denisa Stancu-Dumitru
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Homogeneous Neumann Boundary Condition

EXISTENCE OF GLOBAL SOLUTIONS FOR A PREY–PREDATOR MODEL WITH CROSS-DIFFUSION

2010 ◽  
Vol 03 (02) ◽  
pp. 161-172 ◽  
Author(s):  
SHENGHU XU ◽  
WEIDONG LV
Keyword(s):  
Neumann Boundary Condition ◽  
Space Dimension ◽  
Existence Of Solutions ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Energy Estimates ◽  
Cross Diffusion ◽  
Global Existence Of Solutions ◽  
Homogeneous Neumann Boundary Condition ◽  
Predator Model

In this paper, a ratio-dependent prey–predator model with cross-diffusion and homogeneous Neumann boundary condition is studied. Using the energy estimates and the bootstrap arguments, the global existence of solutions for the model is investigated when the space dimension is less than ten.

Eigenvalues of −Δp − Δq Under Neumann Boundary Condition

2016 ◽  
Vol 59 (3) ◽  
pp. 606-616 ◽  
Author(s):  
Mihai Mihăilescu ◽  
Gheorghe Moroşanu
Keyword(s):  
Boundary Condition ◽  
Eigenvalue Problem ◽  
Neumann Boundary Condition ◽  
Smooth Boundary ◽  
Neumann Boundary ◽  
Careful Analysis ◽  
Full Description ◽  
Open Set ◽  
Homogeneous Neumann Boundary Condition ◽  
Isolated Point

AbstractThe eigenvalue problem −Δpu − Δqu = λ|u|q−2u with p ∊ (1,∞), q ∊ (2,∞), p ≠ q subject to the corresponding homogeneous Neumann boundary condition is investigated on a bounded open set with smooth boundary from ℝN with N ≥ 2. A careful analysis of this problem leads us to a complete description of the set of eigenvalues as being a precise interval (λ1, ∞) plus an isolated point λ = 0. This comprehensive result is strongly related to our framework, which is complementary to the well-known case p = q ≠ 2 for which a full description of the set of eigenvalues is still unavailable.

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