TY  - JOUR
ID  - Hibino2015
LB  - Hibino2015
AU  - Hibino, Masaki
TI  - On the summability of divergent power series solutions for certain first-order linear PDEs
ST  - On the summability of divergent power series solutions for certain first-order linear PDEs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 5
SP  - 595
EP  - 624
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.5.595
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.5.595
AB  - This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations.
KW  - partial differential equation
KW  - divergent power series
KW  - summability
KW  - asymptotic expansion
KW  - analytic continuation
KW  - integro-differential equation
KW  - integral equation
SN  - 1232-9274
ER  -