Abstract
This paper deals with the asymptotic behavior of the solutions of the non-autonomous one-dimensional stochastic Keller-Segel equations defined in a bounded interval with Neumann boundary conditions. We prove the existence and uniqueness of tempered pullback random attractors under certain conditions. We also establish the convergence of the solutions as well as the pullback random attractors of the stochastic equations as the intensity of noise approaches zero.
Highlights
We investigate the long term dynamics of the nonautonomous stochastic Keller-Segel equations defined in a bounded interval I for t > τ with τ ∈ R:
When system (1.1)-(1.2) is supplemented with homogeneous Neumann boundary conditions, by (1.1) we find that u(x, t)dx is constant for all t ≥ τ, I
Given τ ∈ R, consider the following one-dimensional stochastic Keller-Segel equations defined in a bounded interval I = (a1, b1) for t > τ :
Summary
We investigate the long term dynamics of the nonautonomous stochastic Keller-Segel equations defined in a bounded interval I for t > τ with τ ∈ R:. The unknown functions in system (1.1)-(1.2) are u = u(x, t) and ρ = ρ(x, t), a, b and d are fixed positive constants, c : R → R+ is a given function, f : R → R is a given nonlinearity. The deterministic version (i.e., λ = 0) of system (1.1)-(1.2) was proposed by Keller and Segel in [26] to model the aggregation process of cellular slime mold by. Keller-Segel equations, random attractor, asymptotic compactness, upper semi-continuity. The nonlinear function f in (1.1) is called a sensitivity function that is used to model the response of of cells to chemicals
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