Logarithmic decay of hyperbolic equations with arbitrary boundary damping

Uniform energy decay rates of hyperbolic equations with nonlinear boundary and interior dissipation

We consider the problem of uniform stabilization of nonlinear hyperbolic equations, epitomized by the following three canonical dynamics: (1) the wave equation in the natural state space L2(Ω) × H(Ω), under nonlinear (and non-local) boundary dissipation in the Dirichlet B.C., as well as nonlinear internal damping; (2) a corresponding Kirchhoff equation in the natural state space [H(Ω) ∩H1 0 (Ω)...

CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

Study Of Thermoelastic Damping in an Electrostatically Deflected Circular Micro-Plate Using Hyperbolic Heat Conduction Model

Thermoelastic damping (TED) in a circular micro-plate resonator subjected to an electrostatic pressure is studied. The coupled thermo-elastic equations of a capacitive circular micro plate are derived considering hyperbolic heat conduction model and solved by applying Galerkin discretization method. Applying complex-frequency approach to the coupled thermo-elastic equations, TED is obtained for...

Existence and Uniform Decay of Solutions of a Parabolic-Hyperbolic Equation with Nonlinear Boundary Damping and Boundary Source Term

Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...