We consider the initial-value problem of abstract wave equations with weak dissipation. We show that under conditions on the dissipation coefficient and its derivative the solutions to the abstract dissipative equation are closely related to solutions of the free problem multiplied by a decay function. This paper gives the counterpart to a recent paper of T.Yamazaki [Adv. Differential Equ., 11(...

Self-similar propagation of ultrashort, parabolic pulses in a laser resonator is observed theoretically and experimentally. This constitutes a new type of pulse shaping in mode-locked lasers: in contrast to the well-known static (solitonlike) and breathing (dispersion-managed soliton) pulse evolutions, asymptotic solutions to the nonlinear wave equation that governs pulse propagation in most of...

The paper is concerned with Lp error analysis of semi-discrete Galerkin FEMs for nonlinear parabolic equations. The classical energy approach relies heavily on the strong regularity assumption of the diffusion coefficient, which may not be satisfied in many physical applications. Here we focus our attention on a general nonlinear parabolic equation (or system) in a convex polygon or polyhedron ...

Modeling electromagnetic (EM) fields and their interaction with a complex environment is important for developing safe and effective wireless systems. Methods for electromagnetic modeling are computationally intensive, and even small scenario can have long run times. Developments in graphics processing units (GPUs) over the past decade have created an attractive architecture for scientific comp...

This work deals with the derivation of a novel transparent boundary condition (TBC) for the coupling of the standard “parabolic” equation (SPE) in underwater acoustics (assuming cylindrical symmetry) with an elastic parabolic equation (EPE) for modelling the sea bottom extending hereby the existing TBCs for a fluid model of the seabed.

Shallow-water environments typically include sediments containing thin or low-shear layers. Numerical treatments of these types of layers require finer depth grid spacing than is needed elsewhere in the domain. Thin layers require finer grids to fully sample effects due to elasticity within the layer. As shear wave speeds approach zero, the governing system becomes singular and fine-grid spacin...

Acoustic bottom-interacting measurements from the Shallow Water '06 experiment experiment (frequency range 1-20 kHz) are presented. These are co-located with coring and stratigraphic studies showing a thin (approximately 20 cm) higher sound speed layer overlaying a thicker (approximately 20 m) lower sound speed layer ending at a high-impedance reflector (R reflector). Reflections from the R ref...

In this paper, we will present a generalized convolution quadrature for solving linear parabolic and hyperbolic evolution equations. The original convolution quadrature method by Lubich works very nicely for equidistant time steps while the generalization of the method and its analysis to non-uniform time stepping is by no means obvious. We will introduce the generalized convolution quadrature ...

This Postdoctoral Fellowship has three main goals. The first is to quantify the water sediment interaction zone boundary condition for acoustical applications, using theory, numerical computation, experimental results, and constrained inversions. The second is to use range-dependent normal mode and parabolic equation codes along with geoacoustic profiles based on geophysical properties to devel...