On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations

Kunio Ichinobe

Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)

  • Volume: 14, Issue: 3, page 435-458
  • ISSN: 0240-2963

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Ichinobe, Kunio. "On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations." Annales de la Faculté des sciences de Toulouse : Mathématiques 14.3 (2005): 435-458. <http://eudml.org/doc/73653>.

@article{Ichinobe2005,
author = {Ichinobe, Kunio},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Borel summability; integral representation; equations of non-Kovalevski type},
language = {eng},
number = {3},
pages = {435-458},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations},
url = {http://eudml.org/doc/73653},
volume = {14},
year = {2005},
}

TY - JOUR
AU - Ichinobe, Kunio
TI - On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2005
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 14
IS - 3
SP - 435
EP - 458
LA - eng
KW - Borel summability; integral representation; equations of non-Kovalevski type
UR - http://eudml.org/doc/73653
ER -

References

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  1. [Bal] Balser ( W.). — From Divergent Power Series to .Analytic Functions , Springer Lecture Notes, No. 1582 (1994). Zbl0810.34046MR1317343
  2. [Ich 1] Ichinobe ( K.). - The Borel Sum of Divergent Barnes Hypergeometric Series and its Application to a Partial Differential Equation, Publ. Res. Inst. Math. Sci.37, No. 1, p. 91-117 (2001). Zbl0969.33004MR1815996
  3. [Ich 2] -, Integral Representation for Borel Sum of Divergent Solution to a certain non-Kowalevski type Equation, Publ. Res. Inst. Math. Sci.39, No. 4, p. 657-693 (2003). Zbl1063.35049MR2025459
  4. [LMS] Lutz ( D.) , Miyake ( M.), Schäfke ( R.). — On the Borel summability of divergent solutions of the heat equation, Nagoya Math. J.154, p. 1-29 (1999). Zbl0958.35061MR1689170
  5. [Luk] Luke ( Y.L.). — The Special Functions and Their Approximations , Vol IAcademic Press , 1969. Zbl0193.01701MR241700
  6. [Miy] Miyake ( M.). — Borel summability of divergent solutions of the Cauchy problem to non-Kowalevskian equations, Partial differential equations and their applications (Wuhan, 1999), p. 225-239, World Sci. PublishingRiver Edge, NJ ( 1999). Zbl0990.35005MR1742036
  7. [MS] Mathai ( A.M. ) , Saxena ( R.K.). - Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Springer Lecture Notes. No. 348, ( 1973). Zbl0272.33001MR463524

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