Action Functional and Quasi-Potential for the Burgers Equation in a Bounded Interval
In: Communications on pure and applied mathematics, Jg. 64 (2011), Heft 5, S. 649-696
Online
academicJournal
- print, 34 ref
Zugriff:
Consider the viscous Burgers equation ut + f(u)x = ε uxx on the interval [0, 1] with the inhomogeneous Dirichlet boundary conditions u(t, 0) = ρ0, u(t, 1) = ρ1. The flux f is the function f(u) = u(1 ― u), ε > 0 is the viscosity, and the boundary data satisfy 0 < ρ0 < ρ1 < 1. We examine the quasi-potential corresponding to an action functional arising from nonequilibrium statistical mechanical models associated with the above equation. We provide a static variational formula for the quasi-potential and characterize the optimal paths for the dynamical problem. In contrast with previous cases, for small enough viscosity, the variational problem defining the quasi-potential admits more than one minimizer. This phenomenon is interpreted as a nonequilibrium phase transition and corresponds to points where the superdifferential of the quasi-potential is not a singleton.
Titel: |
Action Functional and Quasi-Potential for the Burgers Equation in a Bounded Interval
|
---|---|
Autor/in / Beteiligte Person: | BERTINI, Lorenzo ; DE SOLE, Alberto ; GABRIELLI, Davide ; JONA-LASINIO, Giovanni ; LANDIM, Claudio |
Link: | |
Zeitschrift: | Communications on pure and applied mathematics, Jg. 64 (2011), Heft 5, S. 649-696 |
Veröffentlichung: | Hoboken, NJ: Wiley, 2011 |
Medientyp: | academicJournal |
Umfang: | print, 34 ref |
ISSN: | 0010-3640 (print) |
Schlagwort: |
|
Sonstiges: |
|