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

Mitsuhiro Nakao; Hiroko Okochi

doi:10.1006/jmaa.1996.0054

Anti-periodic solution for u_tt - (σ(u_x))_x - U_xxt = f(x,t)

Mitsuhiro Nakao^*, Hiroko Okochi

^*Corresponding author for this work

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

15 Citations (Scopus)

Abstract

Existence of a smooth anti-periodic solution for the quasilinear equation u_tt - (σ(u_x))_x - u_xxt = 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 language	English
Pages (from-to)	796-809
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	197
Issue number	3
DOIs	https://doi.org/10.1006/jmaa.1996.0054
Publication status	Published - 1996 Feb 1
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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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.",

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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.

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Anti-periodic solution for u_tt - (σ(u_x))_x - U_xxt = f(x,t)

Abstract

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