Stratonovich Solution for the Wave Equation

Numerical solution of the wave equation using shearlet frames

In this paper, using shearlet frames, we present a numerical  method  for solving  the wave equation. We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.

Bessel Beams 2 Solution 2.1 Solution via the Wave Equation

where ρ = √ x2 + y2. Then, the problem is to deduce the form of the radial function f(ρ) and any relevant condition on the wave number kz, and to relate that scalar wave function to a complete solution of Maxwell’s equations. The waveform (1) has both wave velocity and group velocity equal to ω/kz. Comment on the apparent superluminal character of the wave in case that kz < k = ω/c, where c is ...

A Two--Scale Solution Algorithm for the Elastic Wave Equation

Operator-based upscaling is a two-scale algorithm that speeds up the solution of the wave equation by producing a coarse grid solution which incorporates much of the local finescale solution information. We present the first implementation of operator upscaling for the elastic wave equation. By using the velocity-displacement formulation of the three-dimensional elastic wave equation, basis fun...

Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation

Solution Representations for a Wave Equation with Weak Dissipation

parameterized by μ > 0, and prove a representation theorem for its solutions using the theory of special functions. This representation is used to obtain Lp–Lq estimates for the solution and for the energy operator corresponding to this Cauchy problem. Especially for the L2 energy estimate we determine the part of the phase space which is responsible for the decay rate. It will be shown that th...