一类非线性发展方程的全局吸引子

Global Attractors for a Class of Nonlinear Evolution Equations

主要讨论一类非线性发展方程整体强解的长时间行为,利用广义的Gronwall引理,获得了体强解对应解半群的耗散性,然后,通过验证条件(C),证明了系统解半群在D(A)×D(A)上是ω-极限紧,由此得到了全局吸引子的存在性,其中非线性项满足临界指数增长条件.

In this article, we study the long-time behaviors of the strong solutions for a class of nonlinear evolution equations. It is proved that under the natural assumptions, these equations possess the compact attractors, where the nonlinear term f satisfies a critical exponential growth condition.