New asymptotic conservation laws for electromagnetism

Notes on time evolution and conservation laws in electromagnetism

The time evolution of Maxwell’s equations is governed by Ampere’s law ∇ ×H = ∂ ∂t (E + P) + J and Faraday’s Law −∇×E = ∂ ∂t (H+M) +K, where E and H are the electric and magnetic fields, P and M are the electric and magnetic polarization densities, and J and K are the electric and magnetic current densities, respectively. (Magnetic current is the flow of magnetic charge, which is experimentally ...

Asymptotic Conservation Laws in Classical Field Theory.

Asymptotic Conservation Laws in Field Theory

A new approach to the derivation of asymptotic conservation laws in field theory is presented. This approach is based upon the explicit construction of a universal spacetime differential form which plays a central role in the general theory of lowerdegree conservation laws. It is shown that this differential form immediately leads to the standard asymptotic conservations laws for both the Einst...

Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws

This paper studies the asymptotic stability of traveling relaxation shock profiles for hyperbolic systems of conservation laws. Under a stability condition of subcharacteristic type the large time relaxation dynamics on the level of shocks is shown to be determined by the equilibrium conservation laws. The proof is due to the energy principle, using the weighted norms, the interaction of waves ...

A new total variation diminishing implicit nonstandard finite difference scheme for conservation laws

In this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of TVD (total variation diminishing) of the solution, is proposed. This scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. Schemes preserving the essential physical property of TVD are of great importance in practice. Such s...