Gowdy waves as a test-bed for constraint-preserving boundary conditions

Constraint preserving boundary conditions for the Ideal Newtonian MHD equations

Magnetic fields play an important role in the behavior of plasmas and are thought mediate important effects like dynamos in the core of planets and the formation of jets in active galactic nuclei and gamma ray bursts; induce a variety of magnetic instabilities; realize solar flares, etc. (see e.g. [1,2]). Understanding the role of magnetic fields in these and other phenomena have spurred throug...

Asymptotic preserving boundary conditions for kinetic models

Well-posed Initial-boundary Value Problem for a Constrained Evolution System and Radiation-controlling Constraint-preserving Boundary Conditions

A well-posed initial-boundary value problem is formulated for the model problem of vector wave equation subject to the divergence-free constraint. Existence, uniqueness, and stability of the solution is proved by reduction to a system evolving the constraint quantity trivially, namely, the second time derivative of the constraint quantity is zero. A new set of radiationcontrolling constraint-pr...

Constraint-Preserving Boundary Conditions for the Linearized Baumgarte-Shapiro-Shibata-Nakamura Formulation

We derive two sets of explicit homogeneous algebraic constraint-preserving boundary conditions for the second-order in time reduction of the linearized Baumgarte-Shapiro-Shibata-Nakamura BSSN system. Our second-order reduction involves components of the linearized extrinsic curvature only. An initial-boundary value problem for the original linearized BSSN system is formulated and the existence ...

Reaction-diffusion waves with nonlinear boundary conditions

A reaction-diffusion equation with nonlinear boundary condition is considered in a two-dimensional infinite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method. 1. Formulation of the problem. Reaction-diffusion problems with nonlinear boundary conditions arise in various applications. In physiology, such problems describe in particular development of atheroscle...