9 research outputs found
Glauber dynamics in the continuum via generating functionals evolution
We construct the time evolution for states of Glauber dynamics for a spatial
infinite particle system in terms of generating functionals. This is carried
out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a
local (in time) solution which, under certain initial conditions, might be
extended to a global one. An application of this approach to Vlasov-type
scaling in terms of generating functionals is considered as well.Comment: 24 page
Large time existence for 3D water-waves and asymptotics
We rigorously justify in 3D the main asymptotic models used in coastal
oceanography, including: shallow-water equations, Boussinesq systems,
Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre
approximation and full-dispersion model. We first introduce a ``variable''
nondimensionalized version of the water-waves equations which vary from shallow
to deep water, and which involves four dimensionless parameters. Using a
nonlocal energy adapted to the equations, we can prove a well-posedness
theorem, uniformly with respect to all the parameters. Its validity ranges
therefore from shallow to deep-water, from small to large surface and bottom
variations, and from fully to weakly transverse waves. The physical regimes
corresponding to the aforementioned models can therefore be studied as
particular cases; it turns out that the existence time and the energy bounds
given by the theorem are always those needed to justify the asymptotic models.
We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and
remarks added) To appear in Inventione
Statistical dynamics of continuous systems: perturbative and approximative approaches
We discuss general concept of Markov statistical dynamics in the continuum.
For a class of spatial birth-and-death models, we develop a perturbative
technique for the construction of statistical dynamics. Particular examples of
such systems are considered. For the case of Glauber type dynamics in the
continuum we describe a Markov chain approximation approach that gives more
detailed information about statistical evolution in this model.Comment: arXiv admin note: text overlap with arXiv:1109.5094, arXiv:0910.4241,
arXiv:1107.348