Recent progress in the theory of formal solutions for ODE and PDE.

DOI10.1016/S0096-3003(02)00325-9zbMath1054.34142MaRDI QIDQ1408301

Werner Balser, Vladimir Petrov Kostov

Publication date: 15 September 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

Singular perturbationBorel summabilityGevrey orderModified Nagumo normsMultisummability

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30)

Related Items (1)

Flatness-based trajectory planning for diffusion-reaction systems in a parallelepipedon -- A spectral approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A constructive existence proof for first level formal solutions of meromorphic differential equations
• Growth estimates for the coefficients of generalized formal solutions, and representation of solutions using Laplace integrals and factorial series
• Multisummability of formal power series solutions of nonlinear meromorphic differential equations
• Divergent solutions of the heat equation: On an article of Lutz, Miyake and Schäfke
• From divergent power series to analytic functions. Theory and application of multisummable power series
• A new proof of summability of formal solutions of nonlinear meromorphic differential equations
• Multisummability of formal solutions of singular perturbation problems
• Singular perturbation of linear systems with a regular singularity
• Formal power series and linear systems of meromorphic ordinary differential equations
• Singular solutions with asymptotic expansion of linear partial differential equations in the complex domain
• Solutions of first level of meromorphic differential equations
• Summation of Formal Power Series Through Iterated Laplace Integrals.
• Newton polygons and gevrey indices for linear partial differential operators
• On the Borel summability of divergent solutions of the heat equation
• Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space
• Gevrey solutions of singularly perturbed differential equations
• Asymptotic expansion of singular solutions and the characteristic polygon of linear partial differential equations in the complex domain

This page was built for publication: Recent progress in the theory of formal solutions for ODE and PDE.