We consider a mixed problem for a system describing the evolution of sound in a compressible fluid. We describe how to treat a simultaneous exact boundary controllability problem in the sense proposed by J.L. Lions as...We consider a mixed problem for a system describing the evolution of sound in a compressible fluid. We describe how to treat a simultaneous exact boundary controllability problem in the sense proposed by J.L. Lions as well as D. Russell. By using convenient modified multipliers we obtain an observability inequality provided suitable geometric condition on the domain is valid and the speed velocity of the models are related.展开更多
This paper deals with the problem of sharp observability inequality for the 1-D plate equation wtt ＋ wxxxx ＋ q（t, x）w = 0 with two types of boundary conditions w = wxx = 0 or w = wx = 0, and q（t, x） being a suit...This paper deals with the problem of sharp observability inequality for the 1-D plate equation wtt ＋ wxxxx ＋ q（t, x）w = 0 with two types of boundary conditions w = wxx = 0 or w = wx = 0, and q（t, x） being a suitable potential. The author shows that 2 the sharp observability constant is of order exp（C｜｜q｜｜^2/7∞） 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.展开更多
文摘We consider a mixed problem for a system describing the evolution of sound in a compressible fluid. We describe how to treat a simultaneous exact boundary controllability problem in the sense proposed by J.L. Lions as well as D. Russell. By using convenient modified multipliers we obtain an observability inequality provided suitable geometric condition on the domain is valid and the speed velocity of the models are related.
基金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) the National Basic Research Program of China (No. 2011CB808002)
文摘This paper deals with the problem of sharp observability inequality for the 1-D plate equation wtt ＋ wxxxx ＋ q（t, x）w = 0 with two types of boundary conditions w = wxx = 0 or w = wx = 0, and q（t, x） being a suitable potential. The author shows that 2 the sharp observability constant is of order exp（C｜｜q｜｜^2/7∞） 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.
