强阻尼半线性波动方程的全局吸引子

Attractors for Strongly Damped Nonlinear Wave Equation

本文讨论一类带强阻尼项的半线性波动方程的全局吸引子的存在性．首先给出了方程解的存在唯一性定理，建立了解的C°-半群；然后运用Hale提出的a-收缩理论，证明了该类方程存在全局吸引子．

In this paper we study the existence of attractors for a class of strongly damped nonlinear wave equation. First we prove a existence and uniqueness theorem of the solution, so the C°-semigroup of operators is obtained. Finaly, by Hale's a-- contraction theory, we prove that the semigroup has a global attractor.