EXPONENTIAL ENERGY DECAY OF THE EULER-BERNOULLI BEAM WITH SHEAR DIFFUSION THERMAL DISSIPATION/

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 Co-semigroup be ing exponential stable to show that the energy associated with these m odels decays exponentially. A remarkable feature of the proof is that the argument does not need a positive gap of eigenvalues of the relate d operator as before. Therefore, it throws light on the problems in hi gher space dimensions. (C) 1995 Academic Press, Inc.