带有非线性边界条件的弱衰退记忆型非自治经典反应扩散方程解的渐近性

考虑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, 且外力项仅为平移有界而非平移紧时, 弱衰退记忆型非自治经典反应扩散方程解的渐近性态. 应用收缩函数方法和新的先验估计技术, 证明在拓扑空间L²(Ω)×L²_μ(R⁺;L²(Ω))上一致吸引子的存在性, 并给出其拓扑结构.

Asymptotics of Solutions for Non-autonomous Classical Reaction-Diffusion Equation with Nonlinear Boundary Condition and Weak Fading Memory

When the internal nonlinearity and boundary nonlinearity adhered to polynomial growth of arbitrary order as well as the balance condition, and the forcing term was only translation bounded rather than translation compact, we considered the asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary condition and weak fading memory. By using the contractive function method and the new prior estimate technique, we proved the existence and gave topology structure of uniform attractors on topological space L²(Ω)×L²_μ(R⁺;L²(Ω)).