Variational formulation of the Vlasov equation

On the Hamilton-Jacobi Variational Formulation of the Vlasov Equation

In this note we briefly review the Hamilton-Jacobi (HJ) formulation of Vlasov-like systems. This is a general formulation that applies to the Maxwell-Vlasov system and various guiding center and gyrokinetic theories with any number of species. It applies to both nonrelativistic and relativistic versions of these theories and even to the Vlasov-Einstein system. Indeed, it is quite general and ap...

The variational formulation of the Fokker-Planck equation : a summary

A Variational Formulation for the Navier-stokes Equation

Variational Formulation for the Stationary Fractional Advection Dispersion Equation

In this paper a theoretical framework for the Galerkin finite element approximation to the steady state fractional advection dispersion equation is presented. Appropriate fractional derivative spaces are defined and shown to be equivalent to the usual fractional dimension Sobolev spaces H. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. N...

Partial differential equation transform - Variational formulation and Fourier analysis.

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systema...