一类非局部微分方程在Orlicz空间中吸引子的存在性

Existence of attractors for a class of nonlocal partial differential equations in Orlicz spaces

为了刻画带有无上增长限制非线性项的非局部微分方程解的长时间行为,在Orlicz空间中研究了全局吸引子的存在性。首先,证明这类方程在Orlicz空间中解的适定性;其次,得到(L^(2)(Ω),L^(∞)(Ω))-有界吸收集的存在性;最后,通过证明半群的渐近紧性,在任意给定的Orlicz空间中得到了吸引子的存在性。

In order to understand the long-time behavior of a nonlocal partial differential equation without upper growth restriction on nonlinearity,the existence of attractors in Orlicz spaces is considered.Firstly,the well posedness of the solution of this kind of equation in Orlicz spaces is proved.Secondly,the existence of(L^(2)(Ω),L^(∞)(Ω))-bounded absorbing sets is established.Finally,the existence of global attractors in any given Orlicz spaces is obtained by proving the asymptotically compactness of{S(t)};generated by the equations.