We present discrete energy decay results for the Yee scheme applied to Maxwell’s equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme in a nondispersive dielectric. However, energy decay for the Maxwell-Debye and Ma...

This paper concerns the energy conservation for weak solutions to Navier–Stokes–Maxwell system. Although Maxwell equation with hyperbolic nature, we still establish a L q p type condition guarantee validity of equality solutions. We mention that there no regularity assumption on electric field E.

We study spatial localization in the real subcritical Ginzburg-Landau equation ut = m0u + Q(x)u + uxx + d|u|u − |u|u with spatially periodic forcing Q(x). When d > 0 and Q ≡ 0 this equation exhibits bistability between the trivial state u = 0 and a homogeneous nontrivial state u = u0 with stationary localized structures which accumulate at the Maxwell pointm0 = −3d/16. When spatial forcing is i...

The Boltzmann equation for inelastic Maxwell models is considered in order to investigate the dynamics of an impurity (or intruder) immersed in a granular gas driven by a uniform shear flow. The analysis is based on an exact solution of the Boltzmann equation for a granular binary mixture. It applies for conditions arbitrarily far from equilibrium (arbitrary values of the shear rate a) and for ...

this deals with the harmonic forced vibration of a circular plate surface bonded by two piezoelectric layers, based on the kirchhoff plate model. the form of electric potential field in the piezoelectric layer is assumed such that the maxwell static electricity equation is satisfied. the differential equations of motion are solved analytically for clamped edge boundary condition of the plate. t...

We establish a long time soliton asymptotics for a nonlinear system of Maxwell equation coupled to a charged particle. The coupled system has a six dimensional manifold of soliton solutions. We show that in the large time approximation, any solution, with an initial state close to the solitary manifold, is a sum of a soliton and a dispersive wave which is a solution of the free Maxwell equation...

The structure of the Poincaré group gives, under all conditions, an equation of field helicity which reduces to the Maxwell equations and also gives cyclic relations between field components. If the underlying symmetry of special relativity is represented by the Poincaré group, it follows that the Maxwell equations and the cyclic equations are both products of special relativity itself, and bot...

We show that measuring the trajectories of charged particles to nite accuracy leads to the commutation relations needed for the derivation of the free space Maxwell equations using the discrete ordered calculus (DOC). We note that the nite step length derivation of the discrete di erence version of the single particle Dirac equation implies the discrete version of the p; q commutation relations...

In 1872 Ludwig Boltzmann published a lengthy memoir containing two fundamental results: an integro-differential equation describing the time evolution of an ideal gas (Boltzmann equation) and a mathematical argument proving that such evolution must reach, sooner or later, the state of equilibrium described by the Maxwell distribution. The latter achievement, later called the H-theorem, expresse...