Results 41 to 50 of about 2,630 (152)

Analyticity and Gevrey-class regularity for the second-grade fluid equations

, 2009
We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations.
Paicu, Marius, Vicol, Vlad
core   +2 more sources

Umbral Theory and the Algebra of Formal Power Series

Axioms
Umbral theory, formulated in its modern version by S. Roman and G. C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special function theory ...
Roberto Ricci
doaj   +1 more source

New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In this paper, an algebraic decay rate for the radius of spatial analyticity of solutions to the Kawahara equation ∂tu+β∂x5u+α∂x3u+u∂xu=00,β≠ is investigated. With given analytic initial data having a fixed radius of analyticity σ0, we derive an algebraic decay rate σ(t) ~ |t|−1/2 for the uniform radius of spatial analyticity of solutions to the ...
Tegegne Getachew, Jaume Giné
wiley   +1 more source

Newton Polygons and Formal Gevrey Classes

Publications of the Research Institute for Mathematical Sciences, 1990
Untersucht wird ein Cauchyproblem \(Pu=f(t,x)\), \(D^ j_ tu|_{t=0}=g_ j\) (0\(\leq j\leq m-1)\) wobei P die Form hat \(P=D_ t^ m+\sum_{0\leq jm\) ist. Hierzu existiert eine eindeutige Lösung \(u\in G^{\infty}\), nämlich als eine formale Potenzreihe. Gezeigt wird: es ist \(u\in G^ s\) mit \(s=1+1/k_ 1\).
openaire   +3 more sources

Asymptotic Lower Bound on the Spatial Analyticity Radius for Solutions of the Periodic Fifth Order KdV–BBM Equation

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In this work, consideration is given to the initial value problem associated with the periodic fifth‐order KdV–BBM equation. It is shown that the uniform radius of spatial analyticity σ(t) of solution at time t is bounded from below by ct−2/3 (for some c > 0), given initial data η0 that is analytic on the circle and has a uniform radius of spatial ...
Tegegne Getachew, Giovanni P. Galdi
wiley   +1 more source

Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields

, 2018
Let $L_j = \partial_{t_j} + (a_j+ib_j)(t_j) \partial_x, \, j = 1, \dots, n,$ be a system of vector fields defined on the torus $\mathbb{T}_t^{n}\times\mathbb{T}_x^1$, where the coefficients $a_j$ and $b_j$ are real-valued functions belonging to the ...
de Medeira, Cleber, Junior, Alexandre Arias, Kirilov, Alexandre   +2 more
core   +1 more source

Algebraic Lower Bounds on the Spatial Analyticity Radius for Higher Order Nonlinear Schrödinger Equations

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈ℝ,ux,0=u0x, where j ≥ 2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℝ and has a uniform radius of spatial analyticity σ0 in the space variable.
Tegegne Getachew, Birilew Belayneh, Betre Shiferaw, Huaiqin Wu   +3 more
wiley   +1 more source

The Zahorski theorem is valid in Gevrey classes [PDF]

Fundamenta Mathematicae, 1996
The well-known Zahorski theorem [\textit{Z. Zahorski}, Fundam. Math. 34, 183-245 (1947; Zbl 0033.25504)] asserts that for every partition \(\{\Omega,F,G\}\) of \([0,1]\subset\mathbb{R}\), where \(\Omega\) is an open subset of \([0,1]\), \(F\) is a (Baire) first category \(F_\sigma\)-subset of \([0,1]\) and \(G\) is a \(G_\delta\)-subset of \([0,1 ...
Schmets, Jean, Valdivia, Manuel
openaire   +2 more sources

de Sitter State in Heterotic String Theory

Fortschritte der Physik, Volume 72, Issue 11, November 2024.
Abstract Recent no‐go theorems have ruled out four‐dimensional classical de Sitter vacua in heterotic string theory. On the other hand, the absence of a well‐defined Wilsonian effective action and other related phenomena also appear to rule out such time‐dependent vacua with de Sitter isometries, even in the presence of quantum corrections.
Stephon Alexander, Keshav Dasgupta, Archana Maji, Pichai Ramadevi, Radu Tatar   +4 more
wiley   +1 more source