On multisummability of formal solutions with logarithm terms for some linear partial differential equations

Hiroshi Yamazawa

doi:10.1619/fesi.60.371

On multisummability of formal solutions with logarithm terms for some linear partial differential equations

Hiroshi Yamazawa

Department of Engineering and Design

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper we consider formal solutions of the following form for some linear partial differential equations: û(t, x) = ∑_i≥1 ∑_k≤mi u_{i, k}(x)tⁱ (log t)^k. Under the same conditions as those in Ōuchi [8], we show multisummability of the formal solutions û(t, x). It is our key of proofs to find a solution of exponential growth for convolution equations with polynomial coefficients with respect to y via the change of variable log t = y.

Original language	English
Pages (from-to)	371-406
Number of pages	36
Journal	Funkcialaj Ekvacioj
Volume	60
Issue number	3
DOIs	https://doi.org/10.1619/fesi.60.371
Publication status	Published - 2017 Jan 1

Keywords

Asymptotic expansion
Formal solutions
Multisummability

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

Access to Document

10.1619/fesi.60.371

Cite this

@article{4518c6da31a44bdb847233474e5b2db3,

title = "On multisummability of formal solutions with logarithm terms for some linear partial differential equations",

abstract = "In this paper we consider formal solutions of the following form for some linear partial differential equations: {\^u}(t, x) = ∑i≥1 ∑k≤mi ui, k(x)ti (log t)k. Under the same conditions as those in Ōuchi [8], we show multisummability of the formal solutions {\^u}(t, x). It is our key of proofs to find a solution of exponential growth for convolution equations with polynomial coefficients with respect to y via the change of variable log t = y.",

keywords = "Asymptotic expansion, Formal solutions, Multisummability",

author = "Hiroshi Yamazawa",

year = "2017",

month = jan,

day = "1",

doi = "10.1619/fesi.60.371",

language = "English",

volume = "60",

pages = "371--406",

journal = "Funkcialaj Ekvacioj",

issn = "0532-8721",

publisher = "Mathematical Society of Japan - Kobe University",

number = "3",

}

TY - JOUR

T1 - On multisummability of formal solutions with logarithm terms for some linear partial differential equations

AU - Yamazawa, Hiroshi

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper we consider formal solutions of the following form for some linear partial differential equations: û(t, x) = ∑i≥1 ∑k≤mi ui, k(x)ti (log t)k. Under the same conditions as those in Ōuchi [8], we show multisummability of the formal solutions û(t, x). It is our key of proofs to find a solution of exponential growth for convolution equations with polynomial coefficients with respect to y via the change of variable log t = y.

AB - In this paper we consider formal solutions of the following form for some linear partial differential equations: û(t, x) = ∑i≥1 ∑k≤mi ui, k(x)ti (log t)k. Under the same conditions as those in Ōuchi [8], we show multisummability of the formal solutions û(t, x). It is our key of proofs to find a solution of exponential growth for convolution equations with polynomial coefficients with respect to y via the change of variable log t = y.

KW - Asymptotic expansion

KW - Formal solutions

KW - Multisummability

UR - http://www.scopus.com/inward/record.url?scp=85040518938&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040518938&partnerID=8YFLogxK

U2 - 10.1619/fesi.60.371

DO - 10.1619/fesi.60.371

M3 - Article

AN - SCOPUS:85040518938

SN - 0532-8721

VL - 60

SP - 371

EP - 406

JO - Funkcialaj Ekvacioj

JF - Funkcialaj Ekvacioj

IS - 3

ER -

On multisummability of formal solutions with logarithm terms for some linear partial differential equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this