Related papers: Hybrid resonance and long-time asymptotic of the s…
The Maxwell's equations are solved when it has an inhomogeneous terms as a source. The solution is very general in a sense that it handles arbitrary current source and anisotropic media. The calculation is carried out in the k-domain after…
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…
We derive precise late-time asymptotics for solutions to the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes including as special cases the Schwarzschild and Reissner-Nordstrom families of black holes.…
An intense X wave propagating perpendicularly to dc magnetic field is unstable with respect to a parametric decay into an electron Bernstein wave and a lower-hybrid wave. A modified theory of this effect is proposed that extends to the…
The existence and the properties of isolated solutions to the relativistic Vlasov-Maxwell system with initial data on the backward hyperboloid $t=-\sqrt{1+|x|^2}$ are investigated. Isolated solutions of Vlasov-Maxwell can be defined by the…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
We study the long-time asymptotic behavior of solutions u of the Hamilton-Jacobi equation u_t(x,t)+H(x,Du(x,t))=0 in \Omega \times (0,\infty), where \Omega is a bounded open subset of R^n, with Hamiltonian H=H(x,p) being convex and coercive…
Equilibrium equations for magnetically confined, axisymmetric plasmas are derived by means of the energy-Casimir variational principle in the context of Hall magnetohydrodynamics (MHD). This approach stems from the noncanonical Hamiltonian…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
Solar prominences are partially ionised plasmas displaying flows and oscillations. These oscillations show time and spatial damping and, commonly, have been explained in terms of magnetohydrodynamic (MHD) waves. We study the spatial damping…
We obtain and study static, spherically symmetric solutions for the Einstein - generalized Maxwell field system in 2n dimensions, with possible inclusion of a massless scalar field. The generalization preserves the conformal invariance of…
We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with a $3 \times 3$ Lax pair. We use the derived representation to obtain formulas for the long-time asymptotics.
A number of physical processes in laser-plasma interaction can be described with the two-fluid plasma model. We report on a solver for the three-dimensional two-fluid plasma model equations. This solver is particularly suited for simulating…
Heating and ionization are among the most fundamental processes in relativistic laser--solid interactions; however, their spatiotemporal evolution remains challenging to capture experimentally. Here we present detailed diagnosis of…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
In the paper, we develop spectral theory to analyze the sharp asymptotic behavior of solutions to the Boltzmann equation around global Maxwellians in a three-dimensional infinite layer $\mathbb{R}^2\times (-1,1)$. The isothermal diffuse…
In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates…
Astrophysical plasmas are subject to a tight connection between magnetic fields and the diffusion of particles, which leads to an anisotropic transport of energy. Under the fluid assumption, this effect can be reduced to an…
We consider a nonlinear optical system in general, and a broad aperture laser in particular in a resonator where the diffraction coefficients are of opposite signs along two transverse directions. The system is described by the hyperbolic…
In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in R^3. This representation leads to a…