Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations

The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations. Key words Computational quasi-stability - Computational stability - Forced dissipative nonlinear evolution equation - Explicit difference scheme This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCX1-10-07), the National Natural Science Foundation of China (Grant Nos, 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001).

Long-time Dynamics for Thermoelastic Bresse System of Type Ⅲ

This paper considers the thermoelastic beam system of type Ⅲ with friction dissipations acting on the whole system. By using the methods developed by Chueshov and Lasiecka, we get the quasi-stability property of the system and obtain the existence of a global attractor with finite fractal dimension. Result on exponential attractors of the system is also proved.

Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay

This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.

Computational stability of the forced dissipative nonlinear atmospheric equations

A new concept of computational quasi-stability (CQS) is introduced to study the computational stability (CS) of the forced dissipative nonlinear (FDN) evolution equations. Based on the concept, the CQS criterion of difference scheme of FDN atmospheric equations is obtained. So it provides the theoretical basis for designing the computational stable difference scheme of FDN atmospheric equations.

On Robustness of Orbit Spaces for Partially Hyperbolic Endomorphisms

In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse limit space） M^f of f is topologically quasi-stable under C^0-small perturbations in the following sense： For any covering endomorphism g C^0-close to f, there is a continuous map φ from M^9 to Π-∞^∞ M such that for any {yi}i∈z∈φ（M^9）, yi＋1 and f（yi） differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense： For any pseudo-orbit {xi}i∈z, there is a sequence of points {yi}i∈z tracing it, in which yi＋1 is obtained from f（yi） by a motion along the center direction.