Anti-periodic solution for utt - (σ(ux))x - Uxxt = f(x,t)

Mitsuhiro Nakao, Hiroko Okochi

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Existence of a smooth anti-periodic solution for the quasilinear equation utt - (σ(ux))x - uxxt = f(x,t) in [0,π] × R with the boundary condition u(0,t) = u(π,t) = 0 is proved for a class of σ(v) including σ(v) = v/ √1 + v2, where f(x, t) is a given anti-periodic function in t.

Original languageEnglish
Pages (from-to)796-809
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume197
Issue number3
DOIs
Publication statusPublished - 1996 Feb 1
Externally publishedYes

Fingerprint

Anti-periodic Solution
Quasilinear Equations
Periodic Functions
Boundary conditions
Class

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Anti-periodic solution for utt - (σ(ux))x - Uxxt = f(x,t). / Nakao, Mitsuhiro; Okochi, Hiroko.

In: Journal of Mathematical Analysis and Applications, Vol. 197, No. 3, 01.02.1996, p. 796-809.

Research output: Contribution to journalArticle

Nakao, Mitsuhiro ; Okochi, Hiroko. / Anti-periodic solution for utt - (σ(ux))x - Uxxt = f(x,t). In: Journal of Mathematical Analysis and Applications. 1996 ; Vol. 197, No. 3. pp. 796-809.
@article{5d7f692f859f433a8268b7cb46f5243c,
title = "Anti-periodic solution for utt - (σ(ux))x - Uxxt = f(x,t)",
abstract = "Existence of a smooth anti-periodic solution for the quasilinear equation utt - (σ(ux))x - uxxt = f(x,t) in [0,π] × R with the boundary condition u(0,t) = u(π,t) = 0 is proved for a class of σ(v) including σ(v) = v/ √1 + v2, where f(x, t) is a given anti-periodic function in t.",
author = "Mitsuhiro Nakao and Hiroko Okochi",
year = "1996",
month = "2",
day = "1",
doi = "10.1006/jmaa.1996.0054",
language = "English",
volume = "197",
pages = "796--809",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - Anti-periodic solution for utt - (σ(ux))x - Uxxt = f(x,t)

AU - Nakao, Mitsuhiro

AU - Okochi, Hiroko

PY - 1996/2/1

Y1 - 1996/2/1

N2 - Existence of a smooth anti-periodic solution for the quasilinear equation utt - (σ(ux))x - uxxt = f(x,t) in [0,π] × R with the boundary condition u(0,t) = u(π,t) = 0 is proved for a class of σ(v) including σ(v) = v/ √1 + v2, where f(x, t) is a given anti-periodic function in t.

AB - Existence of a smooth anti-periodic solution for the quasilinear equation utt - (σ(ux))x - uxxt = f(x,t) in [0,π] × R with the boundary condition u(0,t) = u(π,t) = 0 is proved for a class of σ(v) including σ(v) = v/ √1 + v2, where f(x, t) is a given anti-periodic function in t.

UR - http://www.scopus.com/inward/record.url?scp=0030080064&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030080064&partnerID=8YFLogxK

U2 - 10.1006/jmaa.1996.0054

DO - 10.1006/jmaa.1996.0054

M3 - Article

VL - 197

SP - 796

EP - 809

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 3

ER -