On singularly perturbed partial integro-differential equations with irregular singularity

DOI10.1007/s10883-007-9018-4zbMath1135.35088OpenAlexW2128104677MaRDI QIDQ2466407

Stéphane Malek

Publication date: 14 January 2008

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10883-007-9018-4

zbMATH Keywords

asymptoticsperturbation\(k\)-summabilityglobal Cauchy-Kowalewski theoremirregular typesingular perturbed partial integro-differential equation

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Singular perturbations in context of PDEs (35B25) Partial functional-differential equations (35R10) Series solutions to PDEs (35C10) Asymptotic expansions of solutions to PDEs (35C20)

Related Items (7)

On Gevrey functional solutions of partial differential equations with Fuchsian and irregular singularities ⋮ On the parametric Stokes phenomenon for solutions of singularly perturbed linear partial differential equations ⋮ On \(q\)-asymptotics for linear \(q\)-difference-differential equations with Fuchsian and irregular singularities ⋮ On the summability of formal solutions for doubly singular nonlinear partial differential equations ⋮ On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces ⋮ On singularly perturbed \(q\)-difference-differential equations with irregular singularity ⋮ Gevrey properties and summability of formal power series solutions of some inhomogeneous linear Cauchy-Goursat problems

Cites Work

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• The Gevrey asymptotics in the case of singular perturbations
• Multisummability of formal solutions of singular perturbation problems
• On the summability of formal solutions in Liouville-Green theory
• Singularly perturbed problems in partial differential equations: A survey
• On the summability of the formal solutions for some PDEs with irregular singularity
• Multisummability of formal power series solutions of partial differential equations with constant coefficients
• Formal power series and linear systems of meromorphic ordinary differential equations
• On a conjecture of Wolfgang Wasow in linear turning point theory
• Gevrey solutions of singularly perturbed differential equations

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