q-analogue of summability of formal solutions of some linear q-difference-differential equations

• Autorzy: Tahara H. , Yamazawa H.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.5.713

• Języki publikacji: EN

Abstrakty

EN

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(t, z) one can construct an actual holomorphic solution which admits X(t, z) as a q-Gevrey asymptotic expansion of order 1.

Słowa kluczowe

EN

q-difference-differential equations; summability; formal power series solutions; q-Gevrey asymptotic expansions; q-Laplace transform

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 5
• Strony: 713--738
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Tahara H.

• Sophia University Department of Information and Communication Sciences Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan

autor

Yamazawa H.

• Shibaura Institute of Technology College of Engineer and Design Minuma-ku, Saitama-shi, Saitama 337-8570, Japan

Bibliografia

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