Related papers: Propagation Estimates for the Boson Star Equation
We present a scheme for numerically solving Maxwell's equations in a weakly perturbed spacetime without introducing the usual geometric optics approximation. Using this scheme, we study light propagation through a spherical perturbation of…
This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of $\mathbb{R}^{P}$ $(P=2,3)$ with a thin layer. We use a method based on hierarchical variational equations to derive asymptotic…
We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different…
We consider the Hamiltonian system of scalar wave field and a single nonrelativistic particle coupled in a translation invariant manner. The particle is also subject to a confining external potential. The stationary solutions of the system…
We study the small dispersion limit of the intermediate long wave (ILW) equation, specifically on a class of well-behaved initial conditions $u_0$ where the number of solitons in the solution increases without bound. First, we conduct a…
Discoveries of fundamental limits for the rates of physical processes, from the speed of light to the Lieb-Robinson bound for information propagation, often lead to breakthroughs in the our understanding of the underlying physics. Here we…
We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…
We consider the time-dependent Schr\"odinger equation that is generated on the bosonic Fock space by a long-range quantum many-body Hamiltonian. We derive the first bound on the maximal speed of particle transport in these systems that is…
In the standard form of the relativistic heat equation used in astrophysics, information propagates instantaneously, rather than being limited by the speed of light as demanded by relativity. We show how this equation nonetheless follows…
We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at…
Equations of light, propagating from quasar to observer on earth, are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This…
The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle dispersion and propagation across interfaces with…
The Lorentz covariant theory of propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses is constructed. The theory is based on the Lienard-Wiechert…
We study the noncommutative $U(1)$ gauge theory on the $\kappa$-Minkowski space-time at the semiclassical approximation. We construct exact solutions of the deformed Maxwell equations in vacuum, describing localized signals propagating in a…
In this paper, a two-component variant of the Degasperis-Procesi equation on the real line is discussed. Applying Kato's theory, we first prove the local well-posedness for the equation under consideration in $H^s\times H^{s-1}$, for $s\geq…
This paper is concerned with the spatial propagation of nonlocal dispersal equations with bistable or multistable nonlinearity in exterior domains. We obtain the existence and uniqueness of an entire solution which behaves like a planar…
We are concerned with large-time behaviors of solutions for Vlasov--Navier--Stokes equations in two dimensions and Vlasov-Stokes system in three dimensions including the effect of velocity alignment/misalignment. We first revisit the…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
In a recent Letter, Cowsik, Ratnam and Bhattacharjee (1996a) have built a dynamically self-consistent spatial distribution of particles of galactic dark matter. They have come up with the rather unorthodox conclusion that the mean velocity…
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…