The paper is concerned with analysis of a Wigner-Fokker-Planck equation with a nonlocal perturbation that consists both conservative and dissipative as well as nonlinear non-local effects. We first show that the system has a finite-time blow-up phenomenon. We then introduce a variational steepest descent approximation scheme for the system. At each step, the scheme minimizes an energy functional with respect to the Kantorovich functional associated with a certain cost function which is inspired by the rate functional in the Freidlin-Wentzell theory of large deviations for the underlying stochastic system.
Name | CASA-report |
---|
Volume | 1313 |
---|
ISSN (Print) | 0926-4507 |
---|