Results 31 to 40 of about 544 (183)

Opérateurs semi-classiques de classe Gevrey dans le domaine complexe

, 2023
International audienceWe study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of
Johannes Sjöstrand, Hitrik, Michael, Richard Lascar, Sjöstrand, Johannes, Michael Hitrik, Maher Zerzeri, Lascar, Richard, Zerzeri, Maher   +7 more
core   +1 more source

Solvability of a system of totally characteristic equations related to Kahler metrics

Electronic Journal of Differential Equations, 2017
We consider a system of equations composed of a higher order singular partial differential equation of totally characteristic type and several higher order non-Kowalevskian linear equations. This system is a higher order version of a system that arose
Jose Ernie C. Lope, Mark Philip F. Ona
doaj  

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

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

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

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

Linearization of hyperbolic resonant fixed points of diffeomorphisms with related Gevrey estimates in the planar case

Electronic Journal of Differential Equations, 2017
We show that any germ of smooth hyperbolic diffeomophism at a fixed point is conjugate to its linear part, using a transformation with a Mourtada type functions, which (roughly) means that it may contain terms like $x \log |x|$.
Patrick Bonckaert, Vincent Naudot
doaj  

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

Gevrey regularity for integro-differential operators

, 2015
We prove for some singular kernels K(x, y) that viscosity solutions of the integro-differential equation. ∫Rn[u(x+y)+u(x-y)-2u(x)]K(x,y)dy=f(x) locally belong to some Gevrey class if so does f.
A. Fiscella, Fiscella, Alessio, Albanese, Guglielmo, Valdinoci, Enrico, G. Albanese, E. Valdinoci   +5 more
core   +1 more source