Temat: series solutions - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On k-summability of formal solutions for certain partial differential operators with polynomial coefficients
Autorzy:: Ichinobe, K.
Miyake, M.
Powiązania:: https://bibliotekanauki.pl/articles/255468.pdf
Data publikacji:: 2015
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: k-summability
Cauchy problem
power series solutions
successive approximation
Opis:: We study the k-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in t. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.
Źródło:: Opuscula Mathematica; 2015, 35, 5; 625-653
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: q-analogue of summability of formal solutions of some linear q-difference-differential equations
Autorzy:: Tahara, H.
Yamazawa, H.
Powiązania:: https://bibliotekanauki.pl/articles/1397578.pdf
Data publikacji:: 2015
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: q-difference-differential equations
summability
formal power series solutions
q-Gevrey asymptotic expansions
q-Laplace transform
Opis:: 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.
Źródło:: Opuscula Mathematica; 2015, 35, 5; 713-738
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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