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Comment on “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator”
International Journal of Mathematics and Mathematical Sciences, 2018 The results of three papers, in which the author inadvertently overlooks certain deficiencies in the descriptions of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a complex Banach space ...
Marat V. Markin
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Exponentially long time stability near an equilibrium point for non--linearizable analytic vector fields [PDF]
, 2004 We study the orbit behavior of a germ of an analytic vector field of $(C^n,0)$, $n \geq 2$. We prove that if its linear part is semisimple, non--resonant and verifies a Bruno--like condition, then the origin is effectively stable: stable for finite but ...
Carletti, Timoteo
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Gevrey class regularity of the magnetohydrodynamics equations [PDF]
The ANZIAM Journal, 2002 AbstractIn this article, we use the method of Foias and Temam to show that the strong solutions of the time-dependent magnetohydrodynamics equations in a periodic domain are analytic in time with values in a Gevrey class of functions. As immediate corollaries we find that the solutions are analytic in Hr-norms and that the solutions become smooth ...
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Quasi-analyticity in Carleman ultraholomorphic classes [PDF]
, 2010 We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors.
Lastra, Alberto, Sanz, Javier
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Propagation of Gevrey Regularity for a Class of Hypoelliptic Equations [PDF]
Transactions of the American Mathematical Society, 1996 We prove results on the propagation of Gevrey and analytic wave front sets for a class of C ∞ C^\infty hypoelliptic equations with double characteristics.
Bove, Antonio, Tartakoff, David S.
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Gevrey class regularity for parabolic equations
Differential and Integral Equations, 2001 We consider the regularity of parabolic equations. We obtain that the solution belongs to Gevrey class 2 up to the boundary if functions in the equation belong to Gevrey class 2 in all dependent variables.
Lee, Pei-Ling, Guo, Yung-Jen Lin
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On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations [PDF]
, 2010 We consider the Euler equations in a three-dimensional Gevrey-class bounded domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of the solution, up to the boundary, with an explicit estimate on the rate of decay of the Gevrey ...
Baouendi M S Goulaouic C +18 more
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Open Mathematics, 2019 It is shown that, if all weak solutions of the evolution ...
Markin Marat V.
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Double exponential stability of quasi-periodic motion in Hamiltonian systems [PDF]
, 2016 We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval ...
A. Bounemoura +18 more
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