Left Definite Theory for Second Order Differential Operators with Mixed Boundary Conditions

AbstractLeft definite theory of regular self-adjoint operators in a Sobolev space was developed a few years ago when the boundary conditions were separated, the separation being necessary in order to properly define the Sobolev inner product. We show how this may be extended when the boundary conditions are not separated, but when evaluations at both ends are mixed together. There are essentially three cases which arise: First when a coefficient matrix is nonsingular, second when it is singular but not 0, third when it is 0. The middle case does not arise under separated conditions

Magnetohydrodynamics and Plasma Cosmology

We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the excitation of cosmological perturbations in anisotropic spacetimes, in the presence of an ambient magnetic field. Acoustic, electromagnetic (e/m) and fast-magnetosonic modes, propagating normal to the magnetic field, can be excited, resulting in several implications of cosmological significance.Comment: 9 pages, RevTeX, To appear in the Proceedings of the Peyresq X Meeting, IJTP Conference Serie