Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients

@article{Michalik2012MultisummabilityOF,
  title={Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients},
  author={Sławomir Michalik},
  journal={Journal of Dynamical and Control Systems},
  year={2012},
  volume={18},
  pages={103-133}
}
  • S. Michalik
  • Published 2012
  • Mathematics
  • Journal of Dynamical and Control Systems
We consider the Cauchy problem for a general inhomogeneous linear partial differential equation with constant coefficients in two complex variables. We obtain necessary and sufficient conditions for the multisummability of formal solutions in terms of analytic continuation properties and growth estimates of some functions connected with the inhomogeneity. The results are presented in the general framework of 1/p-fractional equations. 
Analytic and summable solutions of inhomogeneous moment partial differential equations
We study the Cauchy problem for a general inhomogeneous linear moment partial differential equation of two complex variables with constant coefficients, where the inhomogeneity is given by the formal
Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients
We consider the Cauchy problem for linear moment partial differential equations with constant coefficients in two complex variables. We construct an integral representation of the solution of this
Gevrey Order and Summability of Formal Series Solutions of some Classes of Inhomogeneous Linear Partial Differential Equations with Variable Coefficients
We 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
Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations
Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on
Entire Solutions of Linear Systems of Moment Differential Equations and Related Asymptotic Growth at Infinity
  • A. Lastra
  • Mathematics
    Differential Equations and Dynamical Systems
  • 2022
The general entire solution to a linear system of moment differential equations is obtained in terms of a moment kernel function for generalized summability, and the Jordan decomposition of the
Gevrey Properties and Summability of Formal Power Series Solutions of Some Inhomogeneous Linear Cauchy-Goursat Problems
  • Pascal Remy
  • Mathematics
    Journal of Dynamical and Control Systems
  • 2019
In this article, we investigate the Gevrey and summability properties of the formal power series solutions of some inhomogeneous linear Cauchy-Goursat problems with analytic coefficients in a
On Singularly Perturbed Linear Initial Value Problems with Mixed Irregular and Fuchsian Time Singularities
We consider a family of linear singularly perturbed PDE depending on a complex perturbation parameter $$\epsilon $$ϵ. As in the former study (Lastra and Malek in J Differ Equ 259(10):5220–5270, 2015)
On parametric multisummable formal solutions to some nonlinear initial value Cauchy problems
We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter ϵ whose coefficients depend holomorphically on (ϵ,t)$(\epsilon,t)$ near the origin in

References

SHOWING 1-10 OF 27 REFERENCES
On the Summability of Formal Solutions of Linear Partial Differential Equations
Abstract.We investigate the existence and the Borel summability of formal power series in one variable with holomorphic coefficients, solutions of linear partial differential equations which are not
Summability and fractional linear partial differential equations
We consider the Cauchy problem for Kowalevskaya-type fractional linear partial differential equations with constant coefficients in two complex variables. We show that the solutions can be
Summability of Formal Power-Series Solutions of Partial Differential Equations with Constant Coefficients
We study Gevrey properties and summability of power series in two variables that are formal solutions of a Cauchy problem for general linear partial differential equations with constant coefficients.
Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients
In an earlier paper, the first author showed that certain normalized formal solutions of homogeneous linear partial differential equations with constant coefficients are multisummable, with a
Summability of Solutions of the Heat Equation with Inhomogeneous Thermal Conductivity in Two Variables
We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the
Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations
Basic Properties of Solutions.- Singularities of First Kind.- Highest-Level Formal Solutions.- Asymptotic Power Series.- Integral Operators.- Summable Power Series.- Cauchy-Heine Transform.-
Power Series Solutions of the Inhomogeneous Heat Equation
We investigate formal solutions of the inhomogeneous heat equation, where the inhomogenuity is a -summable formal power series in with coefficients that are holomorphic in a disc.
...
1
2
3
...