Related papers: Well-posedness for an hyperbolic-hyperbolic-ellipt…
There is an increasing reliance on mathematical modelling to assist in the design of piezoelectric ultrasonic transducers since this provides a cost-effective and quick way to arrive at a first prototype. Given a desired operating envelope…
There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…
The dynamics of cold strongly magnetized plasma -- traditionally the domain of force-free electrodynamics -- has recently been reformulated in terms of symmetries and effective field theory, where the degrees of freedom are the momentum and…
The derivation of reduced MHD models for fusion plasma is here formulated as a special instance of the general theory of singular limit of hyperbolic system of PDEs with large operator. This formulation allows to use the general results of…
In this paper, we study a hyperbolic-parabolic coupled system arising in nonlinear three-dimensional thermoelasticity. We establish the global well-posedness and asymptotic behavior of solutions. Our main result shows that, a thermoelastic…
We consider existence and uniqueness for several examples of linear parabolic equations formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation, an equation posed on a bulk domain, a novel coupled…
This work aims at providing a mathematical and numerical framework for the analysis on the effects of pulsed electric fields on biological media. Biological tissues and cell suspensions are described as having a heteregeneous permittivity…
Thermodynamics and dynamics of a classical two-dimensional system with dipole-like isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical…
We describe a new model for the study of weakly-collisional, magnetized plasmas derived from exploiting the separation of the dynamics parallel and perpendicular to the magnetic field. This unique system of equations retains the particle…
Local well-posedness for a nonlinear parabolic-hyperbolic coupled system modelling Micro-Electro-Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has…
We show that the system of equations describing a magnetoviscoelastic fluid in three dimensions can be cast as a quasilinear parabolic system. Using the theory of maximal $L_p$-regularity, we establish existence and uniqueness of local…
In this paper, we study the MHD equations with small viscosity and resistivity coefficients, which may be different. This is a typical setting in high temperature plasmas. It was proved that the MHD equations are globally well-posed if the…
The stability of the system is an important part of the research on differential dynamical systems. This paper considers a pointwise hyperbolic system defined on a connected open subset N of a compact smooth Riemannian manifold M. The…
We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the…
We study well-posedness and long time behavior of the nonlinear Vlasov-Poisson- Fokker-Planck system with an external confining potential. The system describes the time evolution of particles (e.g.$\,\,$in a plasma) undergoing diffusion,…
Multibody dynamics simulation plays an important role in various fields, including mechanical engineering, robotics, and biomechanics. Setting up computational models however becomes increasingly challenging as systems grow in size and…
We describe here a model for inelastic collisions for electronic excitation and deexcitation processes in a general, multifluid plasma. The model is derived from kinetic theory, and applicable to any mixture and mass ratio. The principle of…
Equations describing plasma equilibria are derived from the total energy of the system. The MHD equilibrium is shown to hold even for systems where the magnetic field may locally vanish. Through conservation of helicity, confinement is…
In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device has two…
The hybrid Vlasov-Maxwell system of equations is suitable to describe a magnetized plasma at scales of the order of or larger than proton kinetic scales. An exact stationary solution is presented by revisiting previous results with a…