Abstract
This paper deals with the problem of sharp observability inequality for the 1-D plate equation w tt + w xxxx + q(t, x)w = 0 with two types of boundary conditions w = w xx = 0 or w = w x = 0, and q(t, x) being a suitable potential. The author shows that the sharp observability constant is of order \(\exp \left( {C\left\| q \right\|_\infty ^{\tfrac{2} {7}} } \right)\) for ‖q‖∞ ≥ 1. The main tools to derive the desired observability inequalities are the global Carleman inequalities, based on a new point wise inequality for the fourth order plate operator.
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Project supported by 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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Fu, X. Sharp observability inequalities for the 1-D plate equation with a potential. Chin. Ann. Math. Ser. B 33, 91–106 (2012). https://doi.org/10.1007/s11401-011-0689-5
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DOI: https://doi.org/10.1007/s11401-011-0689-5