一类非线性积分微分方程的全局吸引子

Global Attractors for a Class of Non Linear Integro-Differential Equations

采用一种新的方法,通过对如下初边值问题u_(tt)-Δu-γΔu_t-ωΔu_(tt)-? integral from 0 to t k(t-τ)ψ(u(τ),?u(τ))dτ-h(x,t,u,?u,u_t,?u_t)u_t-g(x,t,u,?u,u_t,?u_t)u+f(u)=σ(x),?(x,t)∈Ω×R^+进行研究,证明了一类非线性积分微分方程在D(A)×D(A)上的全局吸引子,其中h下方有界,非线性项f满足临界指数增长条件,积分项满足指数衰减条件。

In this paper,we adopt a new method to study the initial-boundary value problem as follows：u_（tt）-Δu-γΔu_t-ωΔu_（tt）-？ integral from 0 to t k（t-τ）ψ（u（τ）,？u（τ））dτ-h（x,t,u,？u,u_t,？u_t）u_tg（x,t,u,？u,u_t,？u_t）u＋f（u）=σ（x）,？（x,t）∈Ω×R~＋ and prove the existence of the global attractorΛfor a class of nonlinear integro-differential equations in D（A）×D（A）,where his bounded below,the nonlinear termfsatisfies a critical growth exponential condition and the integral term satisfies the condition of exponential decay.