Singularities of Maxwell interface problems
Singularities of Maxwell interface problems
We investigate time harmonic Maxwell equations in heterogeneous media, where the permeability μ and the permittivity ε are piecewise constant. The associated boundary value problem can be interpreted as a transmission problem. In a very natural way the interfaces can have edges and corners. We give a detailed description of the edge and corner singularities of the electromagnetic fields.
Singularities of Maxwell’s system in non-hilbertian Sobolev spaces
We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space and an explicit singular one.
Soliton-pair Propagation under Thermal Bath Effect
We consider two atomic transitions excited by two variable laser fields in a three-level system. We study the soliton-pair propagation out of resonance and under thermal bath effect. We present general analytical implicit expression of the soliton-pair shape. Furthermore, we show that when the coupling to the environment exceeds a critical value, the soliton-pair propagation through three-level atomic system will be prohibited.
Solutions for a class of integro-differential equations with time periodic coefficients.
Solutions globales du système de Maxwell dans un milieu ferromagnétique
Solutions of initial value problems for a pair of linear first order ordinary differential systems with interface-spatial conditions.
Solutions of inverse problems with potential application for breast tumour detection using microwave measurements.
Solutions to a nonlinear drift-diffusion model for semiconductors.
Solutions to Deconvolution Equations Using Nonperiodic Sampling.
Solutions to Maxwell equations for an electromagnetic beam injected into a plasma.
Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg–Landau equation
We study solutions of the 2D Ginzburg–Landau equation subject to “semi-stiff” boundary conditions: Dirichlet conditions for the modulus, , and homogeneous Neumann conditions for the phase. The principal result of this work shows that there are stable solutions of this problem with zeros (vortices), which are located near the boundary and have bounded energy in the limit of small . For the Dirichlet boundary condition (“stiff” problem), the existence of stable solutions with vortices, whose energy...
Solvability of a first order system in three-dimensional non-smooth domains
A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain . On the boundary , the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.
Solving heat and wave-like equations using He's polynomials.
Some generalized Poincaré inequalities and applications to problems arising in electromagnetism.
Some initial boundary problems in electrodynamics for canonical domains in quaternions
The initial boundary-transmission problems for electromagnetic fields in homogeneous and anisotropic media for canonical semi-infinite domains, like halfspaces, wedges and the exterior of half- and quarter-plane obstacles are formulated with the use of complex quaternions. The time-harmonic case was studied by A. Passow in his Darmstadt thesis 1998 in which he treated also the case of an homogeneous and isotropic layer in free space and above an ideally conducting plane. For thin layers and free...
Some multiple-part Wiener-Hopf problems in mathematical physics
Some new results in multiphase geometrical optics
Some new results in multiphase geometrical optics
In order to accommodate solutions with multiple phases, corresponding to crossing rays, we formulate geometrical optics for the scalar wave equation as a kinetic transport equation set in phase space. If the maximum number of phases is finite and known a priori we can recover the exact multiphase solution from an associated system of moment equations, closed by an assumption on the form of the density function in the kinetic equation. We consider two different closure assumptions based on delta...
Some rigorous results on the Pauli-Fierz model of classical electrodynamics