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We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this scattering problem, closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the plasma echoes in the two approaches. In particular, we prove a non-perturbative result for the scattering problem.
We provide an exact regular solution of an operator system arising as the prolongation structure associated with the heavenly equation. This solution is expressed in terms of operator Bessel coefficients.
Let $H$ be a norm of ${bf R}^N$ and $H_0$ the dual norm of $H$. Denote by $Delta_H$ the Finsler-Laplace operator defined by $Delta_Hu:=mbox{div},(H( abla u) abla_xi H( abla u))$. In this paper we prove that the Finsler-Laplace operator $Delta_H$ acts
We consider the Cauchy problem for the Burgers hierarchy with general time dependent coefficients. The closed form for the Greens function of the corresponding linear equation of arbitrary order $N$ is shown to be a sum of generalised hypergeometric
We consider an evolution equation with the Caputo-Dzhrbashyan fractional derivative of order $alpha in (1,2)$ with respect to the time variable, and the second order uniformly elliptic operator with variable coefficients acting in spatial variables.
The aim of this paper is to investigate the Cauchy problem for the periodic fifth order KP-I equation [partial_t u - partial_x^5 u -partial_x^{-1}partial_y^2u + upartial_x u = 0,~(t,x,y)inmathbb{R}timesmathbb{T}^2] We prove global well-posedness for