Related papers: Internal free boundary problem for cold plasma equ…
We study the quasineutral limit of the isothermal Euler-Poisson system describing a plasma made of ions and massless electrons. The analysis is achieved in a domain of $\R^3$ and thus extends former results by Cordier and Grenier [Comm.…
An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of vacuum. In particular, physical vacuum, in which the boundary moves with a nontrivial finite…
We review the procedure to construct quasi-free ground states, for real scalar fields whose dynamics is dictated by the Klein-Gordon equation, on standard static Lorentzian manifolds with a time-like boundary. We observe that, depending on…
A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the…
So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface…
Nonlinear regimes of one-dimensional parametric instabilities of long-wave plasma waves are considered for the cases when the average plasma field energy density is less (Zakharov's model) or greater (Silin's model) than the plasma thermal…
Analytical studies of light bending in a dispersive medium near compact objects, e.g., black holes or neutron stars, are most challenged by a suitable definition of the medium. The most realistic model would be a hot magnetized plasma. In…
The unique existence of a weak solution to the homogeneous closed Dirichlet problem on certain D-star-shaped domains is proven for a mixed elliptic-hyperbolic equation. Equations of this kind arise in models for electromagnetic wave…
In this study, the problem of overcoming the infinite energy barrier separating the bradyonic and tachyonic realms is investigated. Making use of the Majorana equation for particles with arbitrary spin and the Heisenberg uncertainty…
In this paper we numerically research the solutions of the phase field system for the spherically symmetric Stefan-Gibbs-Thomson problem in the case of interaction of the free boundaries. We analyze the effect of the soliton type…
In thermal equilibrium the ground state of the plasma of Standard Model particles is determined by temperature and exactly conserved combinations of baryon and lepton numbers. We show that at non-zero values of the global charges a…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…
Plasma-boundaries floating in an ionized gas are usually negatively charged. They accumulate electrons more efficiently than ions which leads to the formation of a quasi-stationary electron film at the boundaries. We propose, in a…
The linearized problem of plasma oscillations in layer (particularly, in thin films) in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the…
The influence of motion of ions and electron temperature on nonlinear one-dimensional plasma waves with velocity close to the speed of light in vacuum is investigated. It is shown that although the wavebreaking field weakly depends on mass…
The speed at which ions enter a sheath is a fundamental property of a plasma that also provides a useful boundary condition in modeling. A recent theory proposed that this can be significantly influenced by an instability-enhanced friction…
We consider a porous media equation with balanced bistable reactions, equipped with some general nonlinear boundary condition. When the coefficient of the reaction term is much larger than that of the diffusion term, we see that, besides…
We consider the three-dimensional incompressible free-boundary Euler equations in a bounded domain and with surface tension. Using Lagrangian coordinates, we establish a priori estimates for solutions with minimal regularity assumptions on…