Asymptotic behavior and positive solutions of a chemical reaction diffusion system

Existence of positive stationary solutions for a reaction-diffusion system

where λ > –π, α >  are constants. By a positive solution, we mean a pair of functions (u,φ) with u,φ ∈ C(, ) ∩ C[, ] is a positive solution of (), if (u,φ) satisfies (), and u,φ ≥ , t ∈ [, ], u,φ ≡ . During the last few decades, concerning local equations, the question of the existence of solutions is one of the important topics, and it therefore has attracted much attention [–]....

Differential Delayed Equations - Asymptotic Behavior of Solutions and Positive Solutions

Brief Summary of Basic Notions For a b R , ∈ , a b < , let ([ ] ) n C a b R , , be the Banach space of the continuous functions from the interval [ ] a b , into n R equipped with the supremum norm | ⋅ | . In the case 0 a r = − < , 0 b = , we shall denote this space as r C , that is, ([ 0] ) n r C C r R := − , , and put 0 sup ( ) r r σ φ φ σ − ≤ ≤ || || = | | for r C φ∈ . If R σ ∈ , 0 A ≥ and ([...

Global Well-posedness and Asymptotic Behavior of Solutions to a Reaction-convection-diffusion Cholera Epidemic Model

In this paper, we study the initial boundary value problem of a reaction-convection-diffusion epidemic model for cholera dynamics, which was developed in [38], named susceptible-infected-recovered-susceptible-bacteria (SIRSB) epidemic PDE model. First, a local well-posedness result relying on the theory of cooperative dynamics systems is obtained. Via a priori estimates making use of the specia...

Asymptotic Behavior of a Periodic Diffusion System

Asymptotic behavior of solutions for a class of predator – prey reaction – diffusion systems with time delays ✩

The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator–prey reaction–diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state ...