@Article{Tahara2015,
author = "Tahara, Hidetoshi and Yamazawa, Hiroshi",
title = "q-analogue of summability of formal solutions of some linear q-difference-differential equations",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "5",
pages = "713--738",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.5.713",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.5.713",
abstract = "Let \(q\gt 1\). The paper considers a linear \(q\)-difference-differential equation: it is a \(q\)-difference equation in the time variable \(t\), and a partial differential equation in the space variable \(z\). Under suitable conditions and by using \(q\)-Borel and \(q\)-Laplace transforms (introduced by J.-P. Ramis and C. Zhang), the authors show that if it has a formal power series solution \(\hat{X}(t,z)\) one can construct an actual holomorphic solution which admits \(\hat{X}(t,z)\) as a \(q\)-Gevrey asymptotic expansion of order \(1\).",
keywords = "\(q\)-difference-differential equations, summability, formal power series solutions, \(q\)-Gevrey asymptotic expansions, \(q\)-Laplace transform",
issn = "1232-9274"
}