volume | PIER Journals

2011-07-27

A Simple Solution for the Damped Wave Equation with a Special Class of Boundary Conditions Using the Laplace Transform

Namik Yener

Prof. Namik Yener

Technology Faculty, Biomedical Engineering Dept.

Kocaeli University

Turkey

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Progress In Electromagnetics Research B, Vol. 33, 69-82, 2011

doi:10.2528/PIERB11040901

Abstract

It is proven that for the damped wave equation when the Laplace transforms of boundary value functions ψ(0,t) and (∂ψ(z,t)/∂z)_z=0 of the solution ψ(z,t) have no essential singularities and no branch points, the solution can be constructed with relative ease. In such a case while computing the inverse Laplace transform, the integrals along the segments on the real line are shown to always cancel. The integrals along the circles C_^→ε and C'_^-ε about the point s=-σ/ε determined by the coefficient of the time derivative in the differential equation and point s=0 are shown to vanish unless Laplace transforms of mentioned boundary value functions have poles at these points. If such poles do exist, the problem is nevertheless one of integration along circles about these poles and then setting the radii of these circles equal to zero in the limit.

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Namik Yener, "A Simple Solution for the Damped Wave Equation with a Special Class of Boundary Conditions Using the Laplace Transform," Progress In Electromagnetics Research B, Vol. 33, 69-82, 2011.
doi:10.2528/PIERB11040901

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