q-ANALOGUE OF SUMMABILITY OF FORMAL SOLUTIONS OF SOME LINEAR q-DIFFERENCE-DIFFERENTIAL EQUATIONS

被引：14
|
作者：
Tahara, Hidetoshi [1 ]
Yamazawa, Hiroshi [2 ]
机构：
[1] Sophia Univ, Dept Informat & Commun Sci, Chiyoda Ku, Tokyo 1028554, Japan
[2] Shibaura Inst Technol, Coll Engineer & Design, Minuma Ku, Saitama, Saitama 3378570, Japan
来源：
OPUSCULA MATHEMATICA | 2015年 / 35卷 / 05期
关键词：
q-difference-differential equations; summability; formal power series solutions; q-Gevrey asymptotic expansions; q-Laplace transform;
D O I：
10.7494/OpMath.2015.35.5.713
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let q > 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 (X) over cap (t; z) one can construct an actual holomorphic solution which admits (X) over cap (t; z) as a q-Gevrey asymptotic expansion of order 1.
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页码：713 / 738
页数：26
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