A study is made of the generation of SH-type wves at the free surface of a layered anlsotroplc elastic medium due to an impulsive stress discontinuity moving with uniform velocity along the interface of the layered medium. The exact solution for the displacement function is obtained by the Laplace and Fourier transforms combined with the modified Cagnlard method. The numerical results for an im...

We show that solutions to Smoluchowski’s equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a selfsimilar profile. This convergence holds in a weighted Sobolev norm which implies the L2 convergence of derivatives up to a certain order k depending on the regularity of the initial condition. We prove...

The eigenvalue approach, using the Laplace and Fourier transforms, has been employed to find the analytical expressions for displacements and stresses at any point, as a result of an inclined line load, of an initially stressed orthotropic elastic medium. A plain strain problem has been studied. The results in the form of displacement and stress components have been obtained and discussed graph...

The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed the probabilistic literature, comparison with quarter analogue model. In this context, our main result is to prove that distribution can indeed be found by solving boundary value problem of same kind as one encountered plane, up various dualities and symmetries. idea start from Fourier (and not Laplace) t...

The time-fractional diffusion-wave equation is considered in a half-plane. The Caputo fractional derivative of the order 0 < α < 2 is used. Several examples of problems with Dirichlet and Neumann boundary conditions are solved using the Laplace integral transform with respect to time and the Fourier transforms with respect to spatial coordinates. The solution is written in terms of the Mittag-L...

My assignment is going to introduce the Mellin transform and its application on harmonic sums [1]. Hjalmar Mellin(1854-1933, [2] for a summary of his works) gave his name to the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. Mellin transform is useful to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete prob...

The object of this article is to present the computational solution of onedimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant extension of a result given earl...

It is shown how to model weakly dissipative free-surface flows using the classical potential flow approach. The Helmholtz–Leray decomposition is applied to the linearized 3D Navier–Stokes equations. The governing equations are treated using Fourier–Laplace transforms. We show how to express the vortical component of the velocity only in terms of the potential and free-surface elevation. A new p...

We revisit the Cauchy problem for the time-fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order b 2 ð0; 2 . By using the Fourier–Laplace transforms the fundamentals solutions (Green functions) are shown to be high transcendental functions of the Wright-type that can be interpreted...

We present a set of new, semi-analytical solutions to simulate three-dimensional contaminant transport subject to first-order chain-decay reactions. The aquifer is assumed to be areally semi-infinite, but finite in thickness. The analytical solution can treat the transformation of contaminants into daughter products, leading to decay chains consisting of multiple contaminant species and various...