There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R...We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R^n （n=2,3）.展开更多
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
基金Foundation item: Supported by the NSF of ChinaSupported by the Prominent Youth from Henan Province(0412000100)
文摘We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R^n （n=2,3）.
