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This work is addressed to establish an observability estimate for stochastic wave equations with non-smooth lower order terms. Moreover, the observability constant is estimated by an explicit function of the norm of the involved coefficients in the equation.
The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invariance of some sets under the flow of these problems and the vacuum isolation of solutions are obtained by introducing a family of potential wells. Then the threshold result of global existence and nonexistence of...
In this paper, we study the periodic controllability of linear evolution equations in Hilbert space. Equivalent conditions for this property are presented. Moreover, applications to both the boundary controlled wave equation and plate equation are given.
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