Boundary Stabilization for the Wave Equation in a Bounded Cylindrical Domain
نویسندگان
چکیده
We provide a polynomial decay rate for the energy of the wave equation with a dissipative boundary condition in a cylindrical trapped domain. A new kind of interpolation estimate for the wave equation with mixed Dirichlet-Neumann boundary condition is established from a construction based on a Fourier integral operator involving a good choice of weight functions.
منابع مشابه
Stabilization of the wave equation with a delay term in the boundary or internal feedbacks
In this paper we consider, in a bounded and smooth domain, the wave equation with a delay term in the boundary condition. We also consider the wave equation with a delayed velocity term and mixed Dirichlet-Neumann boundary condition. In both cases, under suitable assumptions, we prove exponential stability of the solution. These results are obtained by introducing suitable energies and by using...
متن کاملA two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملOn the Numerical Solution of One Dimensional Schrodinger Equation with Boundary Conditions Involving Fractional Differential Operators
In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain with transparent boundary conditions that involves half order fractional derivative in t. Then in three...
متن کاملEnergy Decay Rate for the Kirchhoff Type Wave Equation with Acoustic Boundary
In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with acoustic boundary in a bounded domain in Rn. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.
متن کاملStable numerical coupling of exterior and interior problems for the wave equation
The acoustic wave equation on the whole three-dimensional space is considered with initial data and inhomogeneity having support in a bounded domain, which need not be convex. We propose and study a numerical method that approximates the solution using computations only in the interior domain and on its boundary. The transmission conditions between the interior and exterior domain are imposed b...
متن کامل