Related papers: Propagation Estimates for the Boson Star Equation
We consider the question of scattering for the boson star equation in three space dimensions. This is a semi-relativistic Klein-Gordon equation with a cubic nonlinearity of Hartree type. We combine weighted estimates, obtained by exploiting…
We consider finite-energy solutions to the defocusing nonlinear wave equation in two dimensional space. We prove that almost all energy moves to the infinity at almost the light speed as time tends to infinity. In addition, the…
This work is concerned with the broad question of propagation of regularity for smooth solutions to non-linear Vlasov equations. For a class of equations (that includes Vlasov-Poisson and relativistic Vlasov-Maxwell), we prove that higher…
The work proposes and studies a one-dimensional model, which involves nonlocal interactions and finite propagation speed. It shows that the general reaction-diffusion equation, the Swift-Hohenberg equation and the general…
We establish in this article spreading properties for the solutions of equations of the type $\partial$ t u -- a(x)$\partial$ xx u -- q(x)$\partial$ x u = f (x, u), where a, q, f are only assumed to be uniformly continuous and bounded in x,…
A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…
We prove that if the initial condition of the Swift-Hohenberg equation $\partial_t u(x,t)=\bigl(\epsilon^2-(1+\partial_ x^2)^2\bigr) u(x,t) -u^3(x,t)$ is bounded in modulus by $Ce^{-\beta x}$ as $x\to+\infty $, the solution cannot propagate…
In this paper, we first focus on the speed selection problem for the reaction-diffusion equation of the monostable type. By investigating the decay rates of the minimal traveling wave front, we propose a sufficient and necessary condition…
We prove the well-posedness for the non-cutoff Boltzmann equation with soft potentials when the initial datum is close to the {\it global Maxwellian} and has only polynomial decay at the large velocities in $L^2$ space. As a result, we get…
A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wavefunction is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can…
We investigate the propagation of certain non-plane wave solutions to Maxwell's equations in both flat and curved spacetimes. We find that such solutions (or rather parts of them) exhibit accelerative behaviour, and in particular do not…
We prove that Sobolev norms of solutions to time dependent Schr\"odinger equations for $d$-dimensional $N$-partcles interacting via time dependent two body potentials are bounded in time if certain Lebesgue norms of the potentials are small…
The classical free-space solutions of Maxwell's equations for light propagation in one dimension include wave packets of any shape that travel at the speed of light. This includes highly-localised wave packets that remain localised at all…
The dynamics of Schr\"odinger equation with time dependent potentials of general time dependence is considered. It is shown that for localized in space potentials, there is propagation of regularity which is uniformly bounded in higher…
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…
We calculate the short time and the long time diffusion coefficient of a spherical tracer particle in a polymer solution in the low density limit by solving the Smoluchowski equation for a two-particle system and applying a generalized…
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the…
We consider a tracer particle coupled to a Bose scalar field and study the regime where the field's propagation speed approaches infinity. For initial states devoid of field excitations, we introduce an effective approximation of the…
We consider random Schr\"odinger equations on $\bR^d$ or $\bZ^d$ for $d\ge 3$ with uncorrelated, identically distributed random potential. Denote by $\lambda$ the coupling constant and $\psi_t$ the solution with initial data $\psi_0$.…
In this paper we present thoughtful comments on the paper `Bessel beams and signal propagation' showing that the main claims of that paper are wrong. Moreover, we take the opportunity to show the non trivial and indeed surprising result…