Related papers: Propagation Estimates for the Boson Star Equation
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
A new method for the formal solution of the 2D radiative transfer equation in axial symmetry in the presence of arbitrary velocity fields is presented. The combination of long and short characteristics methods is used to solve the radiative…
In this paper, we consider the wave equation in 3-dimensional space with an energy-subcritical nonlinearity, either in the focusing or defocusing case. We show that any radial solution of the equation which is bounded in the critical…
We construct spherically symmetric boson star solutions in $D \in \{4,5,6\}$ spacetime dimensions, considering the effects of both a quartic self-interaction term and a solitonic potential. We then perform a perturbative analysis,…
The radiation transport problem in the plane-parallel medium with the large velocity gradient is considered. The Sobolev approximation is used. The effects of continuum absorption and line overlap are taken into account. The photon loss…
We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In…
In this paper we continue the study of the defocusing, energy-subcritical nonlinear wave equation with radial initial data lying in the critical Sobolev space. In this case we prove scattering in the critical norm when $3 < p < 5$.
We consider the defocusing energy-critical inhomogeneous nonlinear Schr\"{o}dinger equation (INLS) $iu_t + \Delta u = |x|^{-b}|u|^{k}u$ in $\mathbb{R} \times \mathbb{R}^{n}$ where $n \geq 3$, $0<b<\min(2, n/2)$, and $k=(4-2b)/(n-2)$. We…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
We consider a non-relativistic quantum gas of $N$ bosonic atoms confined to a box of volume $\Lambda$ in physical space. The atoms interact with each other through a pair potential whose strength is inversely proportional to the density,…
We study propagation effects due to the finite speed of light in ionization of extended systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light…
We consider a diffusion process under a local weak H\"{o}rmander condition on the coefficients. We find Gaussian estimates for the density in short time and exponential lower and upper bounds for the probability that the diffusion remains…
We theoretically study the propagation through a resonant absorbing medium of a time-dependent perturbation modulating the amplitude of a continuous wave (cw). Modeling the medium as a system of two-level atoms and linearizing the…
The Vlasov-Poisson-Boltzmann System governs the time evolution of the distribution function for the dilute charged particles in the presence of a self-consistent electric potential force through the Poisson equation. In this paper, we are…
The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. In the dilute regime the equation of state is universal in terms of the gas parameter, i.e. it is the same for different potentials with the same value…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
Space-time wave packets can propagate invariantly in free space with arbitrary group velocity thanks to the spatio-temporal correlation. Here it is proved that the space-time wave packets are stable in dispersive media as well and free from…
Light deflection in the post-linear gravitational field of two bounded point-like masses is treated. Both the light source and the observer are assumed to be located at infinity in an asymptotically flat space. The equations of light…
The dynamics of an initially localized wavepacket is studied for the generalized nonlinear Schroedinger Equation with a random potential, where the nonlinearity term is |\psi|^p*\psi and "p" is arbitrary. Mainly short times for which the…
The state equation of strangeon matter is very stiff due to the non-relativistic nature of and the repulsing interaction between the particles, and pulsar masses as high as $\sim 3M_\odot$ would be expected. However, an adiabatic sound…