Global solutions of a linear Cauchy problem.

DOI10.1016/S0022-1236(02)00067-8zbMath1035.35002OpenAlexW2073797486MaRDI QIDQ1403842

Daniel Gourdin, Mustapha Mechab

Publication date: 4 September 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-1236(02)00067-8

zbMATH Keywords

Gevrey classesCauchy-Kowalewski theoremGlobal existenceNagumo theoremFormal normsMajorant of a series

Mathematics Subject Classification ID

Cauchy-Kovalevskaya theorems (35A10)

Related Items (9)

On analytic continuation of solutions of linear partial differential equations ⋮ Solvability of the cohomological equation for regular vector fields on the plane ⋮ Cauchy problems for hyperbolic systems in \(\mathbb{R}^n\) with irregular principal symbol in time and for \(x \rightarrow \infty \) ⋮ Global Cauchy problems on \(\mathbb{R}^n\) for weakly hyperbolic systems with coefficients admitting superlinear growth for \(| x| \rightarrow \infty\) ⋮ Global in time solutions of evolution equations in scales of Banach function spaces in \(\mathbb R^n\) ⋮ On a global Cauchy-Kowalewski-Nagumo theorem in projective Gevrey space. ⋮ Global analytic solutions of linear problems with shrinking argument. (Solutions analytiques globales de problémes linéaires avec argument absorbant) ⋮ Global Cauchy problems for hyperbolic systems with characteristics admitting superlinear growth for \( |x|\rightarrow \infty \) ⋮ On the summability of formal solutions of linear partial differential equations

Cites Work

• Unnamed Item
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• An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
• On hyperbolic equations with analytic coefficients with respect to the spatial variables
• Le problème de Goursat non linéaire
• Global and local goursat problems in a class of holomorphic or partially holomorphic functions
• Nonlinear Goursat problem in Gevrey spaces for generalized Kirchhoff equations
• Global solutions of the nonlinear Goursat problem in Gevrey classes
• A remark on the Cauchy problem for the differential operator of principal type with polynomial coefficients
• On a global Cauchy-Kowalewski-Nagumo theorem
• Hyperbolic operators with non-Lipschitz ceofficients
• The Cauchy problem in spaces of entire functions
• Équations et systèmes non-linéaires, hyperboliques non-stricts
• Diagonalisation des systèmes quasilinéaires et hyperbolicité non stricte
• A New Proof and Generalizations of the Cauchy-Kowalewski Theorem
• Nonlinear hyperbolic equations

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