Riesz Basis Property and Exponential Stability for One-Dimensional Thermoelastic System with Variable Coefficients

Riesz Basis Property and Exponential Stability of Controlled Euler--Bernoulli Beam Equations with Variable Coefficients

This paper studies the basis property and the stability of a distributed system described by a nonuniform Euler–Bernoulli beam equation under linear boundary feedback control. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. The asymptotic distribution of eigenvalues, the spectrumdetermined growth condition,...

Exponential stability of variable coefficients Rayleigh beams under boundary feedback controls: a Riesz basis approach

In this paper, we study the boundary stabilizing feedback control problem of Rayleigh beams that have non-homogeneous spatial parameters. We show that no matter how non-homogeneous the Rayleigh beam is, as long as it has positive mass density, sti9ness and mass moment of inertia, it can always be exponentially stabilized when the control parameters are properly chosen. The main steps are a deta...

Stability and Riesz Basis Property for General Network of Strings

In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator A. Under certain conditions, we prove that the spectrum of A is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator A,...

General decay of solutions to a one-dimensional thermoelastic beam with variable coefficients

Exponential Stability and Global Attractors for a Thermoelastic Bresse System

We consider the stability properties for thermoelastic Bresse system which describes the motion of a linear planar shearable thermoelastic beam. The system consists of three wave equations and two heat equations coupled in certain pattern. The two wave equations about the longitudinal displacement and shear angle displacement are effectively damped by the dissipation from the two heat equations...