Goong Chen

Modeling stabilization and control of serially connected beams

Many flexible structures consist of a large number of components coupled end to end in the form of a chain. In this paper, we consider the simplest type of such structures which is formed by N seri...

Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities

Abstract Many theorems in convex analysis and quasi-variational inequalities can be derived by using a class of weaker convexity (concavity) conditions which require a functional φ ( x , y ) to be quasi-convex or convex for diagonal entries of certain type. In this paper, we discuss such conditions and use them to generalize several important theorems such as Ky Fans inequality and saddle point theorem and some recent results in quasi-variational inequalities.

Control and Stabilization for the Wave Equation in a Bounded Domain, Part II

The present note makes a further study on the distributed parameter control and stabilization for the wave equation in an earlier article (SIAM J. Control Optim., 17 (1979) pp. 66–81). Decay rates and control time are improved by a new stabilization scheme of combined viscous damping and compensation. A stabilizing control for a regulator problem is also derived.

Exponential decay of energy of evolution equations with locally distributed damping

Consider an evolution equation with energy dissipation, \[ \frac{\partial }{{\partial t}}y( {x,t} ) = Ay( {x,t} ) + By( {x,t} ) \] on a bounded x-domain

A Note on the Boundary Stabilization of the Wave Equation

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Mathematics of Quantum Computation

, where

ALGORITHMS AND VISUALIZATION FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS

By

Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span

signifies a dissipative perturbation to an otherwise energy-conserving system. This dissipation may be due to medium impurities, viscous effects, or artificially imposed dampers and stabilizers. It is distributed over only part of the domain

Analysis designs, and behavior of dissipative joints for coupled beams

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A high-linking algorithm for sign-changing solutions of semilinear elliptic equations

. The question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined.Because of the locally distributed nature of energy dissipation, the problem lacks coercivity and is not directly solvable by energy identities. Thus, to get conditions sufficient for uniform exponential decay, a different approach needs to be taken. Provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorBon the separated eigenmodes or clustered eigenmodes ofA. The main theorems are general enough to treat the wave and bea...