耗散孤立波方程的惯性分形集  

The Inertial Fractal Set of the Dissipative Soliton Equations

作　　者：李庆玉[1] 席泓[2] 

机构地区：[1]重庆商学院基础部,重庆400067 [2]贵州民族学院数学系,贵阳550025

出　　处：《西南师范大学学报（自然科学版）》2000年第6期645-647,共3页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：证明了耗散孤立波方程的惯性分形集的存在性 .主要结果是 :定理　若u0 ∈H10 (Ω) ,v ,β ,α >0 ,其中Ω =[- L2 ,L2 ],L >0 ,则问题ut+vuxxxx+αuux+uxxx+ βu=fu(x ,0 ) =u0u｜ Ω =ux｜ Ω =0生成的半群S(t)在V中关于 (S(t) ,B)The existence of the inertial fractional set is proved for the dissipative soliton equations. The main result is the following theorem.\;Theorem\ Suppose u\-0∈H\+1\-0(Ω), v,β,α>0, where Ω=[-L2, L2] with >0. Then the semigroup S(t) generated by the problemu\-t+vu\-\{xxxx\}+αuu\-x+u\-\{xxx\}+βu=f u(x, 0)=u\-0 u｜\-\-\{Ω\}=u\-x｜\-\-\{Ω\}=0has an inertial fractal set for (S(t), B) in H\+1\-0(Ω)

关 键 词：耗散孤立波 挤压性 惯性分形集 非线性方程 动力系统 

分 类 号：O175.29[理学—数学] O19[理学—基础数学]