相关论文: Boundary value problem of magnetically insulated d…
The paper analyses volt-ampere characteristics of a planar vacuum diode with mono-energetic electrons, emitted by the cathode (an electron beam). The movement of the electron beam in the volume of the diode is described. An analytic…
We investigate the compressible magnetohydrodynamic equations subject to large external potential forces with discontinuous initial data in a three-dimensional bounded domain under Navier-slip boundary conditions. We show the global…
The ideal diode is a theoretical concept that completely conducts the electric current under forward bias without any loss and that behaves like a perfect insulator under reverse bias. However, real diodes have a junction barrier that…
We study the quasineutral limit for the relativistic Vlasov-Maxwell system in the framework of analytic regularity. Following the high regularity approach introduced by Grenier [44] for the Vlasov-Poisson system, we construct local-in-time…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
This paper is the direct-formulation companion to [Burbano-Gallegos, P\'erez-Arancibia, and Turc, ESAIM: M2AN, 60(1):273--315, 2026], which developed indirect combined-field-only boundary integral equations (BIEs) for time-harmonic…
The electromagnetic response of topological insulators is governed by axion electrodynamics, which features a topological magnetoelectric term in the Maxwell equations. As a consequence magnetic fields become the source of electric fields…
When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse…
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…
A non-commutative formula for the isotropic magneto-electric response of disordered insulators under magnetic fields is derived using the methods of non-commutative geometry. Our result follows from an explicit evaluation of the Ito…
We consider viscous free-boundary magnetohydrodynamics(MHD) under vacuum in $\mathbb{R}^3$, especially when vacuum magnetic field is identically zero. It is a central problem in mathematics to perform vanishing viscosity limit to get a…
In this note we consider boundary value problems in electromagnetism. We prove well-posedness results for the time-harmonic Maxwell equations in the setting of Riemannian manifolds. We also consider the eigenvalue problem the homogeneous…
The problem of a spin-free electron with mass $m$, charge $e$ confined onto a ring of radius $R_0$ and with an attractive Dirac delta potential with scaling factor (depth) $\kappa$ in non-relativistic theory has closed form analytical…
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
Topological insulators (TIs) are quantum materials combining insulating bulk properties with conductive surface states protected by time-reversal symmetry. Their unique electromagnetic behavior originates from the topological…
We derive and analyze well-posed, energy- and entropy-stable boundary conditions (BCs) for the two-dimensional linear and nonlinear rotating shallow water equations (RSWE) in vector invariant form. The focus of the study is on subcritical…
We consider a model of axisymmetric neutron star magnetosphere. In our approach, the current density in the region of open field lines is constant and the returning current flows in a narrow layer along the separatrix. In this case, the…
We study the (characteristic) Cauchy problem for the Maxwell-Bloch equations of light-matter interaction via asymptotics, under assumptions that prevent the generation of solitons. Our analysis clarifies some features of the sense in which…
In this paper, we study the existence of nodal solutions for the non-autonomous Schr\"{o}dinger--Poisson system: \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+u+\lambda K(x) \phi u=f(x) |u|^{p-2}u & \text{ in }\mathbb{R}^{3}, \\…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…