A fully discrete nite element method is used to approximate the electric eld equation derived from Maxwell equations in three dimensional polyhedral domains. Optimal energy-norm error estimates are achieved for general Lipschitz polyhedral domains. Optimal L 2-norm error estimates are obtained for convex polyhedral domains. R esum e On r esout, dans un domaine poly edrique, les equations de Max...

We present the covering set of the squared eigenfunctions for a degenerate 3×3 eigenvalue problem. The derivation follows the approach recently outlined by Yang and Kaup on this same equation (J. Math. Phys. 50 023504 (2009)). This eigenvalue problem is important since it serves as the spectral problem for the inverse scattering transform (IST) of the vector NLS equation, the Sasa– Satsuma equa...

Abstract. It is shown that a broad class of generalized Dirichlet series (including the polylogarithm, related to the Riemann zeta-function) can be presented as a class of solutions of the Fourier transformed spatially homogeneous linear Boltzmann equation with a special Maxwell-type collision kernel. The result is based on an explicit integral representation of solutions to the Cauchy problem ...

We consider the quantum nonlinear Schrödinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation for correlation functions simplifies in the small mass limit of the Bose particle. In this limit we describe the correlation functions by the vacuum expectation...

We study the asymptotic regime for the relativistic Vlasov-Maxwell-FokkerPlanck system which corresponds to a mean free path small compared to the Debye length, chosen as an observation length scale, combined to a large thermal velocity assumption. We are led to a convection-diffusion equation, where the convection velocity is obtained by solving a Poisson equation. The analysis is performed in...

Integrating factors and adjoint equations are determined for linear and nonlinear differential equations of an arbitrary order. The new concept of an adjoint equation is used for construction of a Lagrangian for an arbitrary differential equation and for any system of differential equations where the number of equations is equal to the number of dependent variables. The method is illustrated by...

— A new splitting is proposed for solving the Vlasov–Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov–Maxwell system and allows for the construction of arbitrary high order methods by composition (independent of the specific deterministic method used for the discretization of the phase space). Moreover, we show that for a spectral method in space this ...

The Weibel instability is analyzed for quantum plasmas described by the Wigner-Maxwell model. For a suitable class of electromagnetic potentials, the Wigner-Maxwell system is linearized yielding a general dispersion relation for transverse electromagnetic waves. For a double Gaussian equilibrium with temperature anisotropy, the derived dispersion relation generalizes the classical Weibel instab...

The aim of this paper is to review and classify the different methods that have been developed to enable stable long time simulations of the VlasovMaxwell equations and the Maxwell equations with sources. These methods can be classified in two types: field correction methods and sources correction methods. The field correction methods introduce new unknowns in the equations, for which additiona...

Two new two-grid algorithms are proposed for solving the Maxwell eigenvalue problem. The new methods are based on the two-grid methodology recently proposed by Xu and Zhou [Math. Comp., 70 (2001), pp. 17-25] and further developed by Hu and Cheng [Math. Comp., 80 (2011), pp. 1287-1301] for elliptic eigenvalue problems. The new two-grid schemes reduce the solution of the Maxwell eigenvalue proble...