scholarly journals Asymptotic stability of a boundary layer to the Euler--Poisson equations for a multicomponent plasma

2016 ◽  
Vol 9 (3) ◽  
pp. 587-603 ◽  
Author(s):  
Masahiro Suzuki
Keyword(s):  
Boundary Layer ◽  
Asymptotic Stability ◽  
Multicomponent Plasma ◽  
Poisson Equations

Degenerate boundary layers for a system of viscous conservation laws

2016 ◽  
Vol 14 (01) ◽  
pp. 75-99
Author(s):  
Tohru Nakamura
Keyword(s):  
Boundary Layer ◽  
Asymptotic Stability ◽  
Conservation Laws ◽  
Type Inequality ◽  
A Priori Estimate ◽  
Hardy Type Inequality ◽  
Weighted Energy Method ◽  
Boundary Layer Solution ◽  
Viscous Conservation Laws ◽  
Layer Solution

This paper is concerned with existence and asymptotic stability of a boundary layer solution which is a smooth stationary wave for a system of viscous conservation laws in one-dimensional half space. With the aid of the center manifold theory, it is shown that the degenerate boundary layer solution exists under the situation that one characteristic is zero and the other characteristics are negative. Asymptotic stability of the degenerate boundary layer solution is also proved in an algebraically weighted Sobolev space provided that the weight exponent [Formula: see text] satisfies [Formula: see text]. The stability analysis is based on deriving the a priori estimate by using the weighted energy method combined with the Hardy type inequality with the best possible constant.

scholarly journals Stabilization of an Underactuated Surface Vessel Based on Adaptive Sliding Mode and Backstepping Control

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fuguang Ding ◽  
Jing Wu ◽  
Yuanhui Wang
Keyword(s):  
Boundary Layer ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sliding Mode ◽  
Backstepping Method ◽  
Adaptive Function ◽  
Control Laws ◽  
Adaptive Sliding Mode ◽  
Simulation Results ◽  
Surface Vessel

The paper studied controlling problem of an underactuated surface vessel with unknown interferences. It proved that the control problem of underactuated surface vessel can be transformed into the stabilization analysis of two small subsystems. This controller was designed by backstepping method and adaptive sliding mode, was suitable for solving the problem of the control of higher systems, can keep the system global asymptotic stability, and can inhibit unknown interference, and boundary layer can weaken the buffeting generated by sliding mode. The unknown interference was estimated by adaptive function. Finally, the simulation results are given to demonstrate the effectiveness of the proposed control laws.

Sign in / Sign up

Export Citation Format

Share Document