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| Sharp Observability Inequalities for the 1-D Plate Equation with a Potential |
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Citation： |
Xiaoyu FU.Sharp Observability Inequalities for the 1-D Plate Equation with a Potential[J].Chinese Annals of Mathematics B,2012,33(1):91~106 |
| Page view： 3167
Net amount： 2506 |
Authors： |
Xiaoyu FU; |
Foundation： |
the National Natural Science Foundation of China (No. 10901114), the Doctoral Fund for New Teachers of the Ministry of Education of China (No.20090181120084) and the National Basic Research Program of China (No. 2011CB808002). |
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| Abstract： |
This paper deals with the problem of sharp observability inequality for the1-D plate equation wtt + wxxxx + q(t, x)w = 0 with two types of boundary conditionsw = wxx = 0 or w = wx = 0, and q(t, x) being a suitable potential. The author shows thatthe sharp observability constant is of order exp(C_q_2|7∞) for _q_∞ ≥ 1. The main tools toderive the desired observability inequalities are the global Carleman inequalities, based ona new point wise inequality for the fourth order plate operator. |
Keywords： |
Observability inequality, Plate equation, Point-wise estimate, Carleman estimate |
Classification： |
93B05,93B07 |
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