相关论文: Finite Energy Superluminal Solutions of Maxwell Eq…
Garay-Avenda\~no \& Zamboni-Rached (2014) defined two classes of axisymmetric solutions of the free Maxwell equations. We prove that the linear combinations of these two classes of solutions cover all totally propagating time-harmonic…
The new solution of the Einstein equations in empty space is presented. The solution is constructed using Schwarzschild solution but essentially differs from it. The basic properties of the solution are: the existence of a horizon which is…
We give an explicit description of the basic solutions of max-linear systems with two inequalities.
We present general results on exponential decay of finite energy solutions to stationary nonlinear Schr\"odinger equations.
For the plane symmetry we have found the electro-vacuum exact solutions of the Einstein-Maxwell equations and we have shown that one of them is equivalent to the McVittie solution of a charged infinite thin plane. The analytical extension…
A class of exact solutions of the Einstein-Maxwell equations is presented which contains infinite sets of gravitoelectric, gravitomagnetic and electromagnetic multipole moments. The multipolar structure of the solutions indicates that they…
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…
Several exact expansions as well as lower and upperbounds of the Kermack and McKendrick SIR equations are presented.
Mathematical proofs are presented concerning the existence of solutions of the Maxwell equations with suitable boundary conditions. In particular it is stated that the well known "delayed potentials" provide effective solutions of the…
We consider 3D stochastic Landau-Lifshitz-Gilbert equations coupled with the Maxwell equations with the full energy. We have proved the existence and some further regularities of the weak solution.
We investigate the cylindrical class of Newman Tamburino equations in the presence of an aligned Maxwell field. After obtaining a complete integration of the field equations we look at the possible vacuum limits and we examine the…
We report on a new two-parameter class of cosmological solutions to the Einstein-Maxwell equations. The solutions have everywhere regular curvature invariants. We prove that the solutions are geodesically complete and globally hyperbolic.
The space-time focusing of a (continuous) succession of localized X-shaped pulses is obtained by suitably integrating over their speed, i.e., over their axicon angle, thus generalizing a previous (discrete) approach. First, new Superluminal…
We prove new well-posedness results for energy-critical nonlinear Schr\"odinger equations in modulation spaces. This covers initial data with infinite mass and energy. The proof is carried out via bilinear refinements and adapted function…
recent theoretical results show the existence of arbitrary speeds ($0\leq v <\infty$) solutions of the wave equations of mathematical physics. Some recent experiments confirm the results for sound waves. The question arises naturally: What…
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…
Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a {\em pair} of matrix equations. We present a matrix representation of the Maxwell equation…
We discuss invertibility properties for entire finite-energy solutions of the regularized version of a singular Liouvillle equation.
We establish the local-in-time existence of solutions to the relativistic Euler equations representing dynamical liquid bodies in vacuum.
We consider the singular elliptic problem of the form \[ -\Delta u + V(x)u = \mathcal{B}(x)|u|^{2^*-2}u + \frac{\mathcal{A}(x)}{|u|^{2^*}u}, \qquad u\in H^1(M), \] where the coefficients are allowed to have low regularity. Under natural…