衰退记忆型经典反应扩散方程在非线性边界条件下解的渐近性

Asymptotic behavior of solutions for the classical reaction-diffusion equation with nonlinear boundary conditions and fading memory

本文研究了记忆型经典反应扩散方程解的长时间动力学行为.当内部非线性项和边界非线性项均以超临界指数增长并满足一定的平衡条件时,运用抽象函数理论和半群理论,证明了该方程的全局吸引子在L^2(Ω)×L^2μ(R^+;H^1(Ω))中的存在性,此结果改进和推广了一些已有的结果.

In this paper,we study the asymptotic behavior of solutions for the classical reaction-diffusion equation with memory.Through the use of abstract function theory and semigroup theory,the existence of a global attractor in L^2(Ω)×L^2μ(R+;H^1(Ω))is proven when the internal nonlinearity and boundary nonlinearity adhere to polynomial growth of arbitrary order as well as the balance condition.This result extends and improves some known results.