Variational Formulation for the KPZ and Related Kinetic Equations
arXiv:0911.4800 · doi:10.1142/S0218127409024505
Abstract
We present a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a potential we prove some global shift invariance properties previously conjectured by other authors. We also show a few results about the form of the stationary probability distribution function for arbitrary dimensions. The procedure used for KPZ was extended in order to derive more general forms of such a functional leading to other nonlinear kinetic equations, as well as cases with density dependent surface tension.
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- Surface tension of bulky colloids, capillarity under gravity and the microscopic origin of the Kardar-Parisi-Zhang equation
- Combined use of mixed and hybrid finite elements method with domain decomposition and spectral methods for a study of renormalization for the KPZ model