English

Analytic and summable solutions of inhomogeneous moment partial differential equations

Analysis of PDEs 2018-01-12 v2 Complex Variables

Abstract

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 power series. We state sufficient conditions for the convergence, analytic continuation and summability of formal power series solutions in terms of properties of the inhomogeneity. We consider both the summability in one variable t (with coefficients belonging to some Banach space of Gevrey series with respect to the second variable z) and the summability in two variables (t,z).

Keywords

Cite

@article{arxiv.1505.06724,
  title  = {Analytic and summable solutions of inhomogeneous moment partial differential equations},
  author = {Sławomir Michalik},
  journal= {arXiv preprint arXiv:1505.06724},
  year   = {2018}
}

Comments

26 pages. arXiv admin note: substantial text overlap with arXiv:1303.1555