A global attractor for the elastic waveguide model in R-N

作者：Yang Zhijian^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(17): 6640-6661.

DOI：10.1016/j.na.2011.06.045

• The elastic waveguide model
• Cauchy problem
• Infinite-dimensional dynamical system
• Longtime behavior of solutions
• Global attractor

This paper studies the longtime behavior of solutions to the elastic waveguide model in R-N : u(tt) - Delta u - Delta u(tt) + Delta(2)u - Delta u(t) + u(t) + u - Delta g(x, u) = f(x). It proves that when the space dimension N <= 5, under rather mild conditions on g and f the related solution semigroup possesses in phase space with low regularity X-delta = ((H) over dot (2) boolean AND H1+delta) x ((H) over dot (2) boolean AND H-delta), with 0 < delta <= 1, a global attractor which is connected.

• 出版日期2011-12
• 单位郑州大学