Related papers: Well-posedness for an hyperbolic-hyperbolic-ellipt…
A representation of the static MHD equilibrium system in coordinates connected with magnetic surfaces is suggested. It is used for producing families of non-trivial 3D exact solutions of isotropic and anisotropic plasma equilibria in…
The classical two-dimensional one-component plasma is an exactly solvable model, at some special temperature, even when the one-body potential acting on the particles has a quadrupolar term. As a supplement to a recent work of Di Francesco,…
In this paper, we study the well-posedness and exact controllability of a physical model for a food extrusion process in the isothermal case. The model expresses the mass balance in the extruder chamber and consists of a hyperbolic Partial…
Electron-hole systems on a Haldane sphere are studied by exact numerical diagonalization. Low lying states contain one or more types of bound charged excitonic complexes Xk-, interacting through appropriate pseudopotentials. Incompressible…
We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces…
We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose…
We develop an effective field theory approach to inspect the electromagnetic interactions in an electrically neutral plasma, with an equal number of negative and positive charge carriers. We argue that the static equilibrium configurations…
We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…
Interaction of an intense electromagnetic (EM) beam with hot relativistic plasma is investigated. It is shown that the thermal pressure brings about a fundamental change in the dynamics - localized, high amplitude, EM field structures, not…
We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. For initial data in $H^s, s>\frac{d}{2}+1$, the…
The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling…
We introduce a simplified model of the electron-beam/plasma system to model the electrical breakdown caused by the inductive electric field created by a rapidly rising electron beam current. The rigid-beam model is a reduction to the…
We consider a linearized Euler--Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. We present the derivation of the model, and we show its well-posedeness, its strong and polynomial stability…
The aim of this work is to show an abstract framework to analyze a family of linear degenerate parabolic mixed equations. We combine the theory for the degenerate parabolic equations with the classical Babuska-Brezzi theory for linear mixed…
We study the well-posedness and stability of an impedance passive infinite-dimensional linear system under nonlinear feedback of the form $u(t)=\phi(v(t)-y(t))$, where $\phi$ is a monotone function. Our first main result introduces…
We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the…
We present an abstract framework for treating the theory of well-posedness of solutions to abstract parabolic partial differential equations on evolving Hilbert spaces. This theory is applicable to variational formulations of PDEs on…
We study the local-in-time well-posedness for an interface that separates an anisotropic plasma from a vacuum. The plasma flow is governed by the ideal Chew-Goldberger-Low (CGL) equations, which are the simplest collisionless fluid model…
In this work, we study the local wellposedness of the solution to a nonlinear elliptic-dispersive coupled system which serves as a model for a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device…
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…