Related papers: Waves in a random medium: Endpoint Strichartz esti…
The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form $(-\Delta)^\alpha\partial_t u$, $\alpha\in(0,\frac{1}{2})$, in bounded smooth domains of $\Bbb R^3$. It appears that to…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…
This paper is concerned with reaction-diffusion-advection equations in spatially periodic media. Under an assumption of weak stability of the constant states 0 and 1, and of existence of pulsating traveling fronts connecting them, we show…
Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
The one-dimensional propagation of seismic waves with constant Q is shown to be governed by an evolution equation of fractional order in time, which interpolates the heat equation and the wave equation. The fundamental solutions for the…
A wave propagating through a scattering medium typically yields a complex temporal field distribution. Over the years, a number of procedures have emerged to shape the temporal profile of the field in order to temporally focus its energy on…
We consider the wave equation with uncertain initial data and medium, when the wavelength $\varepsilon$ of the solution is short compared to the distance traveled by the wave. We are interested in the statistics for quantities of interest…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…
We use the fractional integrals in order to describe dynamical processes in the fractal media. We consider the "fractional" continuous medium model for the fractal media and derive the fractional generalization of the equations of balance…
Here we study novel effects associated with electromagnetic wave propagation in a Robertson-Walker universe and the Schwarzschild spacetime with a small amount of metric stochasticity. We find that localization of electromagnetic waves…
The distribution function for the intensity of radiation propagating in a random medium is analyzed for arbitrary multiplicity of scattering (for arbitrary relation between the distance of propagation and mean free path), including as…
Motivated by the long-time transport properties of quantum waves in weakly disordered media, the present work puts random Schr\"odinger operators into a new spectral perspective. Based on a stationary random version of a Floquet type…
Impulsive gravitational waves are theoretical models of short but violent bursts of gravitational radiation. They are commonly described by two distinct spacetime metrics, one of local Lipschitz regularity, the other one even…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
The work presented here emanates from questions arising from experimental observations of the propagation of surface water waves. The experiments in question featured a periodically moving wavemaker located at one end of a flume that…
We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and…
We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The waveguide is filled with an isotropic linear dielectric material, with randomly…
In this paper, we investigate the existence and stability of random transition fronts of KPP-type lattice equations in random media, and explore the influence of the media and randomness on the wave profiles and wave speeds of such…
We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with $x$-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was…