کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4592908 | 1335159 | 2006 | 17 صفحه PDF | دانلود رایگان |
This paper proves that any initial condition in the energy space for the plate equation with square root damping on a smooth bounded domain, with hinged boundary conditions ζ=Δζ=0, can be steered to zero by a square integrable input function u supported in arbitrarily small time interval [0,T] and subdomain. As T tends to zero, for initial states with unit energy norm, the norm of this u grows at most like exp(Cp/Tp) for any real p>1 and some Cp>0. Indeed, this fast controllability cost estimate is proved for more general linear elastic systems with structural damping and non-structural controls satisfying a spectral observability condition. Moreover, under some geometric optics condition on the subdomain allowing to apply the control transmutation method, this estimate is improved into p=1 and the dependence of Cp on the subdomain is made explicit. These results are analogous to the optimal ones known for the heat flow.
Journal: Journal of Functional Analysis - Volume 236, Issue 2, 15 July 2006, Pages 592-608