Results 51 to 60 of about 429 (166)
The Metivier inequality and ultradifferentiable hypoellipticity
Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
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Strong unique continuation for higher order elliptic equations with Gevrey coefficients [PDF]
, 2012 We address the strong unique continuation problem for higher order elliptic partial differential equations in 2D with Gevrey coefficients. We provide a quantitative estimate of unique continuation (observability estimate) and prove that the solutions ...
Ignatova, Mihaela +3 more
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Cauchy problem for hyperbolic systems in Gevrey class. A note on Gevrey indices [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 2000 The author considers the hyperbolic system \[ \begin{gathered} [I_4 D_t+ A(t) D_x+ B(t)]u(t,x)= 0,\\ u(0,x)= u_0(x)\end{gathered} \] in \(\Omega= [0,T]\times \mathbb{R}^1_x\) where \(I_4\) denotes the unit matrix of order 4 and \[ A(t)= \begin{pmatrix} \lambda(t) & 1 & 0 & 0\\ 0 &\lambda(t) & a(t) & 0\\ 0 & 0 & \mu(t) & 1\\ 0 & 0 & 0 & \mu(t)\end ...
openaire +2 more sources
Taylor dispersion and phase mixing in the non‐cutoff Boltzmann equation on the whole space
Proceedings of the London Mathematical Society, Volume 129, Issue 1, July 2024.Abstract In this paper we describe the long‐time behavior of the non‐cutoff Boltzmann equation with soft potentials near a global Maxwellian background on the whole space in the weakly collisional limit (that is, infinite Knudsen number 1/ν→∞$1/\nu \rightarrow \infty$). Specifically, we prove that for initial data sufficiently small (independent of the
Jacob Bedrossian +2 more
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Evolution for overdetermined systems in (small) Gevrey classes [PDF]
, 2009 Given a system of linear partial differential operators with constant coefficients whose affine algebraic varieties V have dimension 1, we establish in which classes of (small) Gevrey functions the associated Cauchy problem admits at least one solution ...
BOITI, Chiara, R. Meise
core
Gevrey regularity for the supercritical quasi-geostrophic equation [PDF]
, 2014 In this paper, following the techniques of Foias and Temam, we establish suitable Gevrey class regularity of solutions to the supercritical quasi-geostrophic equations in the whole space, with initial data in “critical” Sobolev spaces.
Biswas, Animikh
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Soft Riemann‐Hilbert problems and planar orthogonal polynomials
Communications on Pure and Applied Mathematics, Volume 77, Issue 4, Page 2413-2451, April 2024.Abstract Riemann‐Hilbert problems are jump problems for holomorphic functions along given interfaces. They arise in various contexts, for example, in the asymptotic study of certain nonlinear partial differential equations and in the asymptotic analysis of orthogonal polynomials. Matrix‐valued Riemann‐Hilbert problems were considered by Deift et al. in
Haakan Hedenmalm
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Well posedness of the Cauchy problem for nonlinear weakly hyperbolic equations [PDF]
, 1999 The authors study well-posedness of the Cauchy problem for several classes of nonlinear (semilinear) weakly hyperbolic equations. It is assumed that the principal part of the operator possesses real characteristic roots of constant multiplicity, and that
ZANGHIRATI, Luisa, CICOGNANI M.
core
Gevrey Order and Summability of Formal Series Solutions of some Classes of Inhomogeneous Linear Partial Differential Equations with Variable Coefficients [PDF]
, 2016 International audienceWe investigate Gevrey order and summability properties of formal power series solutions of some classes of inhomogeneous linear partial differential equations with variable coefficients and analytic initial conditions. In particular,
Remy, Pascal
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Resurgent aspects of applied exponential asymptotics
Studies in Applied Mathematics, Volume 152, Issue 3, Page 974-1025, April 2024.Abstract In many physical problems, it is important to capture exponentially small effects that lie beyond‐all‐orders of an algebraic asymptotic expansion; when collected, the full asymptotic expansion is known as a trans‐series. Applied exponential asymptotics has been enormously successful in developing practical tools for studying the leading ...
Samuel Crew, Philippe H. Trinh
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