Name
Abstract | ||
|---|---|---|
Using a Riesz basis approach, we investigate, in this paper, the exponential stability for a one-dimensional linear thermoelasticity of type III with Dirichlet-Dirichlet boundary conditions. A detailed spectral analysis gives that the spectrum of the system contains two parts: the point and continuous spectrum. It is shown that, by asymptotic analysis, there are three classes of eigenvalues: one is along the negative real axis approaching to - ∞, the second is approaching to a vertical line which parallels to the imagine axis, and the third class is distributed around the continuous spectrum which is an accumulation point of the last classes of eigenvalues. Moreover, it is pointed out that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the energy state space. Finally, the spectrum-determined growth condition holds true and the exponential stability of the system is then established. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/ASCC.2013.6606136 | ASCC |
Keywords | Field | DocType |
riesz basis approach,spectrum-determined growth condition,thermoelasticity,energy state space,eigenvalues,state-space methods,1d linear thermoelasticity,type iii thermoelasticity,asymptotic stability,point spectrum,asymptotic analysis,spectral analysis,imagine axis,exponential stability,dirichlet-dirichlet boundary condition,generalized eigenfunctions,eigenvalues and eigenfunctions,negative real axis,continuous spectrum,heating,control theory,boundary conditions,mathematical model | Boundary value problem,Continuous spectrum,Eigenfunction,Mathematical analysis,Complex plane,Exponential stability,Asymptotic analysis,Limit point,Eigenvalues and eigenvectors,Mathematics | Conference |
Volume | Issue | ISSN |
null | null | null |
ISBN | Citations | PageRank |
978-1-4673-5767-8 | 0 | 0.34 |
References | Authors | |
3 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jing Wang | 1 | 25 | 2.45 |
| Jun-Min Wang | 2 | 219 | 29.95 |