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.

In this paper, we consider the Dirichlet and impedance boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane. These boundary value problems arise in a study of timeharmonic acoustic scattering of an incident eld by a sound-soft, in nite rough surface where the total eld vanishes (the Dirichlet problem) or by an in nite, impedance rough surface where the total ...

The present paper is the first in a series of works devoted to the solvability of the Possio singular integral equation. This equation relates the pressure distribution over a typical section of a slender wing in subsonic compressible air flow to the normal velocity of the points of a wing downwash . In spite of the importance of the Possio equation, the question of the existence of its solutio...

An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are u...

Richardson extrapolation is applied to improve the accuracy of the numerical solution of boundary integral equations. The boundary integral equations arise from a direct boundary integral method for solving a Laplace’s equation interior Dirichlet problem. Specifically, the Richardson extrapolation is used to improve the accuracy of collocation. Numerical justification is provided to support the...

This guide describes a collection of programs for creating and re ning triangulations on surfaces and solving integral equations using collocation methods over these tri angulations The main purpose of this package is to allow for experimentation with numerical methods for solving boundary integral equations that are de ned on piecewise smooth surfaces in R For a general survey of the numerical...

Nonlocal problems is a major research area in many branches of modern physics, biotechnology, chemistry and engineering, which arises when it is impossible to determine the boundary values of unknown function and its derivatives. Increasingly often, there arise problems with nonlocal integral boundary conditions, especially in particle diffusion [1] and heat conduction [2, 3]. Partial different...

Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu,...

We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral boundary condition, with a real parameter. This equivalence allows us to obtain the solution to some problems for non-classical heat equation, the continuous dependence of the solution with...

and a0 is a constant, b is a continuous periodic function of variables x and y, a1 and g are continuous periodic functions. This integral equation appears in exterior boundary value problems for the two-dimensional Helmholtz equation (see [11,15– 17,27]). Constructions of conformal mapping also lead to integral equations of this kind (see [22]). In recent years, the Helmholtz equation and its n...