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Nonlocal wave turbulence in the Charney-Hasegawa-Mima equation: a short review
Nonlocal wave turbulence short review
2010/12/28
Rossby wave turbulence, as modelled by the Charney-Hasegawa-Mima (CHM) equation, is nonlo-
cal in scale. As a result, the formal stationary Kolmogorov-Zakharov solutions of the Rossby wave kinetic eq...
Convergence of the Dirichlet solutions of the very fast diffusion equation
very fast diffusion equation Dirichlet problem
2011/2/21
For any −1 < m < 0, μ > 0, 0 ≤ u0 ∈ L∞(R) such that u0(x) ≤ (μ0|m||x|) 1 m for any |x| ≥ R0 and some constants R0 > 1 and 0 < μ0 ≤ μ, and f, g ∈C([0,∞)) such that f(t), g(t) ≥ μ0 on [0,∞) we pro...
The Gould-Hopper Polynomials in the Novikov-Veselov equation
Gould-Hopper Polynomials Novikov-Veselov equation
2010/11/10
We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov (NV) equation. The root dynamics of the $\sigma$-flow in the NV equation is studied using the GH polynomials and then the L...
We establish a decoupling result for the P and S waves of linear, isotropic elasticity, in the setting of twice-differentiable Lam´e parameters.
Non-uniform dependence on initial data for the CH equation on the line
CH equation integrable non-periodic Cauchy problem Sobolev spaces
2010/12/10
For s > 3=2 two sequences of CH solutions living in a bounded set of the Sobolev space Hs(R) are constructed, whose distance at the initial time is converging to zero while at any later time is bounde...
On long-time decay for modified Klein-Gordon equation
Klein-Gordon equation relativistic equations resolvent spectral representa-tion
2010/12/6
We obtain a dispersive long-time decay in weighted energy norms for solutions of the Klein-Gordon equation in a moving frame. The decay extends the results of Jensen, Kato and Murata for the equations...
Preliminary group classification for generalized inviscid Burger's equation
Burgers’ equation Equivalence transformations Lie symmetries
2010/12/9
Preliminary group classification for a class of generalized inviscid Burger’s equa-tions in the general form ut+g(x, u)ux = f(x, u) is given and additional equivalence transformations are found. Adduc...
Generalized Landau-Lifshitz Equation into $S^n$
Generalized Landau-Lifshitz Equation $S^n$
2010/12/6
In this paper, a type of integrable evolution equation–the generalized Landau-Lifshitz equation into Sn is considered. We deal with this equation from a geometric point of view by rewriting it in a ge...
An equation for the general Ramsey number R(p1,p2,...pt;r)
equation general Ramsey number R
2010/12/1
Abstract:The Ramsey number is a valve value such that as long as the cardinality n of the n-set V is no less than R,however all the r-subsets of V are distributed into t boxes, V will always have a pr...
Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit
Spectral methods Boltzmann equation cut-off assumption Fokker-Planck-Landau equation
2010/12/14
In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the socalled grazing collision limit.