Exponential Energy Decay of the Euler-Bernoulli Beam with Shear Diffusion/Thermal Dissipation

✍ Scribed by Z.Y. Liu; S.M. Zheng

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 328 KB
• Volume: 196
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1995.1420

✦ Synopsis

In this paper, we study the asymptotic behavior of the Euler-Bernoulli elastic beam model coupled a diffusion and/or a dissipation process. We then use a necessary and sufficient condition for a (C_{0})-semigroup being exponential stable to show that the energy associated with these models decays exponentially. A remarkable feature of the proof is that the argument does not need a positive gap of eigenvalues of the related operator as before. Therefore, it throws light on the problems in higher space dimensions. C 1995 Academic Press, Inc.