Related papers: On a wave equation with singular dissipation
We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…
This expository note gives a digest version of Hormander's propagation of singularities theorem for the wave equation.
The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…
Sampling equation method is presented to look for exact solutions of nonlinear differential equations. Application of this approach to one of the extensive chaos model is considered. Exact solutions of this model in travelling wave are…
In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity $u_{tt} - \Delta u = u^{p}$ in three space dimensions. We show that for generic large initial…
The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…
In this work we give new regularity results of solutions for the linear wave equation set in a nonsmooth cylindrical domain. Different types of conditions are imposed on the boundary of the singular domain. Our study is performed in some…
In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…
This article presents a new scheme for studying the dynamics of a quintic wave equation with nonlocal weak damping in a 3D smooth bounded domain. As an application, the existence and structure of weak, strong, and exponential attractors for…
The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
We give a way to recover time-dependent singular coefficients of the wave-equation in the one-dimensional case.
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
We construct solutions to nonlinear wave equations that are singular along a prescribed noncharacteristic hypersurface which is the graph of a function satisfying not the Eikonal but another partial differential equation of the first order.…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group…