Related papers: An alternative formulation of the magnetostatic bo…
A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is…
We derive a variational formulation for thin film magnetization problems in type-II superconductors written in terms of two variables, the electric field and the magnetization function. A numerical method, based on this formulation, makes…
We examine the transient scattered and transmitted fields generated when an incident electromagnetic wave impinges on a dielectric scatterer or a coated conductor embedded in an infinite space. By applying a boundary-field equation method,…
A magnetic helicity integral is proposed which can be applied to domains which are not magnetically closed, i.e. have a non-vanishing normal component of the magnetic field on the boundary. In contrast to the relative helicity integral,…
In this work, we study the solvability of a boundary value problem for the magneto-hydrostatic equations originally proposed by Grad and Rubin in the late 50's. The proof relies on a fixed point argument which combines the so-called current…
We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem
This paper concerns the initial-boundary value problem to 2D micropolar equations without angular viscosity in a smooth bounded domain. It is shown that such a system admits a unique and global weak solution. The main idea of this paper is…
We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact…
The perturbation of a magnetostatic field by a toroid made of a homogeneous anisotropic magnetic material was formulated using the solutions of the Laplace equation in the toroidal coordinate system. That was straightforward in the region…
We introduce a simple approach to evaluate the magnetic field distribution around superconducting samples, based on the London equations; the elementary variable is the vector potential. This procedure has no adjustable parameters, only the…
We study an inverse boundary value problem with partial data in an infinite slab in $\mathbb{R}^{n}$, $n\geq 3$, for the magnetic Schr\"{o}dinger operator with an $L^{\infty}$ magnetic potential and an $L^{\infty}$ electric potential. We…
This short article contains the derivation of a general formula for the magnetostatic field in the neighbourhood of an axis of symmetry.
We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic…
We survey recent results on inverse boundary value problems for the magnetic Schroedinger equation.
The retarded vector potential of a point magnetic dipole with an arbitrary time dependence undergoing accelerated relativistic motions is derived. A novel expression for the angular distribution of the radiated power of an arbitrary moving…
On the basis of generalization of upper and lower solution method to the singular two point boundary value problems, the existence theorem of solutions for the system, which models a process of magnetic insulation in plasma is proved.
A new boundary value problem for partial differential equations is discussed. We consider an arbitrary solution of an elliptic or parabolic equation in a given domain and no boundary conditions are assumed. We study which restrictions the…
An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were…