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Register a new userComparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation
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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.
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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.
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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. This equation describes the propagation of stress pulses in a viscoelastic medium. Its properties are intermediate between those of parabolic and hyperbolic equations. In this paper, we construct and investigate a fundamental solution of the Cauchy problem, prove existence and uniqueness theorems for such equations.
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