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Browsing by Subject "q-difference-differential equations"

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    Item type:Article, Access status: Open Access ,
    q-analogue of summability of formal solutions of some linear q-difference-differential equations
    (2015) Tahara, Hidetoshi; Yamazawa, Hiroshi
    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.