Multisummability of formal power series solutions of partial differential equations with constant coefficients
From MaRDI portal
Publication:1880770
DOI10.1016/j.jde.2004.02.002zbMath1052.35048OpenAlexW2054688431MaRDI QIDQ1880770
Publication date: 1 October 2004
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2004.02.002
Related Items
On parametric multisummable formal solutions to some nonlinear initial value Cauchy problems ⋮ On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables ⋮ Summability of divergent solutions of the \(n\)-dimensional heat equation ⋮ Gevrey order and summability of formal series solutions of some classes of inhomogeneous linear partial differential equations with variable coefficients ⋮ Symmetry reductions and exact solutions to the Sharma-Tasso-Olever equation ⋮ On singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularities ⋮ Gevrey order and summability of formal series solutions of certain classes of inhomogeneous linear integro-differential equations with variable coefficients ⋮ Multisummability in Carleman ultraholomorphic classes by means of nonzero proximate orders ⋮ On Gevrey functional solutions of partial differential equations with Fuchsian and irregular singularities ⋮ Gevrey regularity of the solutions of some inhomogeneous semilinear partial differential equations with variable coefficients ⋮ Asymptotic existence theorem for formal solutions with singularities of nonlinear partial differential equations via multisummability ⋮ Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients ⋮ Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations ⋮ Time integration algorithm based on divergent series resummation, for ordinary and partial differential equations ⋮ On the summability of the solutions of the inhomogeneous heat equation with a power-law nonlinearity and variable coefficients ⋮ Lie symmetry analysis and exact solutions of the Sawada--Kotera equation ⋮ Borel summability of the heat equation with variable coefficients ⋮ On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems ⋮ Summable solutions of the Goursat problem for some partial differential equations with constant coefficients ⋮ On singularly perturbed partial integro-differential equations with irregular singularity ⋮ Nonlinear evolution PDEs in \(\mathbb R^+ \times \mathbb C^d\): existence and uniqueness of solutions, asymptotic and Borel summability properties ⋮ Analytic and Summable Solutions of Inhomogeneous Moment Partial Differential Equations ⋮ Asymptotic Analysis and Summability of Formal Power Series ⋮ Summability of formal solutions of linear partial differential equations with divergent initial data ⋮ Asymptotic existence theorems for formal power series whose coefficients satisfy certain partial differential recursions ⋮ The Borel summable solutions of heat operators on a real analytic manifold ⋮ On the multisummability of divergent solutions of linear partial differential equations with constant coefficients ⋮ Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. I ⋮ Summable solutions of some partial differential equations and generalised integral means ⋮ Gevrey properties and summability of formal power series solutions of some inhomogeneous linear Cauchy-Goursat problems ⋮ Gevrey index theorem for the inhomogeneous n-dimensional heat equation with a power-law nonlinearity and variable coefficients ⋮ The Stokes phenomenon for certain partial differential equations with meromorphic initial data ⋮ Symmetry reductions, exact solutions, stability analysis and conservation laws of time-fractional Sharma–Tasso–Olever equation ⋮ Summability of the formal power series solutions of a certain class of inhomogeneous nonlinear partial differential equations with a single level ⋮ Summability in general Carleman ultraholomorphic classes ⋮ Strongly regular sequences and proximate orders ⋮ On the summability of formal solutions of linear partial differential equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations
- 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
- Divergence property of formal solutions for singular first order linear partial differential equations
- Multisummability of formal solutions of singular perturbation problems
- Singular perturbation of linear systems with a regular singularity
- Summability of divergent series
- Formal power series and linear systems of meromorphic ordinary differential equations
- Addendum to my paper: A DIFFERENT CHARACTERIZATION OF MULTI-SUMMABLE POWER SERIES
- Newton polygons and gevrey indices for linear partial differential operators
- On the Borel summability of divergent solutions of the heat equation
- Convergent Liouville–Green expansions for second-order linear differential equations, with an application to Bessel functions
- Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space
- Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables
- Gevrey solutions of singularly perturbed differential equations