# Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients

@inproceedings{Michalik2013AnalyticSO, title={Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients}, author={Sławomir Michalik}, year={2013} }

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 problem and study its analyticity. As a result we derive a characterisation of multisummable formal solutions of the Cauchy problem.

## 28 Citations

Gevrey estimates for certain moment partial differential equations

- Mathematics
- 2018

We consider the Cauchy problem for inhomogeneous linear moment differential equations with holomorphic time dependent coefficients. Using such tools as the formal norms, theory of majorants and the…

The Stokes Phenomenon for Some Moment Partial Differential Equations

- MathematicsJournal of Dynamical and Control Systems
- 2018

We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the…

k-summability of Formal Solutions for Linear PDEs with Constant Coefficients

- Mathematics
- 2014

We shall study the k-summability of formal solutions for the Cauchy problem of linear partial differential equations with constant coefficients. We employ the method of successive approximation for…

ON k-SUMMABILITY OF FORMAL SOLUTIONS FOR CERTAIN PARTIAL DIFFERENTIAL OPERATORS WITH POLYNOMIAL COEFFICIENTS

- Mathematics
- 2015

We study the k-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in t. We employ the method of…

On the k -Summability of Formal Solutions for a Class of Higher Order Partial Differential Equations with Time-Dependent Coefficients

- Mathematics
- 2017

We study the k-summability of divergent formal solutions to the Cauchy problem of a class of higher order linear partial differential equations with time-dependent coefficients. The problem is…

Entire Solutions of Linear Systems of Moment Differential Equations and Related Asymptotic Growth at Infinity

- MathematicsDifferential 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…

On k-summability of formal solutions for certain partial differential operators with polynomial coefficients

- Mathematics
- 2015

We study the \(k\)-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in \(t\). We employ the…

On the Formal Solutions of a Type of Singular Partial Differential Equations

- Mathematics
- 2021

In this paper, we research a partial differential equation with three complex variables. According to the theory of singular differential equations, it is proved by direct calculation that it has a…

Summability of Formal Solutions for Some Generalized Moment Partial Differential Equations

- Mathematics
- 2020

The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the…

Hyperasymptotic Solutions for Certain Partial Differential Equations

- Mathematics
- 2017

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The…

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