Degenerate anisotropic elliptic problems and magnetized plasma simulations

Efficient Numerical Methods for Strongly Anisotropic Elliptic Equations

In this paper, we study an efficient numerical scheme for a strongly anisotropic elliptic problem which arises, for example, in the modeling of magnetized plasma dynamics. A small parameter ε induces the anisotropy of the problem and leads to severe numerical difficulties if the problem is solved with standard methods for the case 0 < ε 1 . An Asymptotic-Preserving scheme is therefore introduce...

Buoyancy Instabilities in Degenerate, Collisional, Magnetized Plasmas

In low-collisionality plasmas, anisotropic heat conduction due to a magnetic field leads to buoyancy instabilities for any nonzero temperature gradient. We study analogous instabilities in degenerate collisional plasmas, i.e., when the electron collision frequency is large compared to the electron cyclotron frequency. Although heat conduction is nearly isotropic in this limit, the small residua...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Eigenvalue Problems for Degenerate Nonlinear Elliptic Equations in Anisotropic Media

We study nonlinear eigenvalue problems of the type −div(a(x)∇u) = g(λ,x,u) in RN , where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequal...

The Features of the Angular Spectrum of Scattered Radiation by Turbulent Collisional Anisotropic Magnetized Plasma

Statistical characteristics of the angular power spectrum of scattered radiation for power law spectrum of electron density fluctuations in turbulent collisional anisotropic magnetized plasma are considered.