Existence of an anti-periodic solution for the quasilinear wave equation with viscosity

Mitsuhiro Nakao

doi:10.1006/jmaa.1996.0465

Existence of an anti-periodic solution for the quasilinear wave equation with viscosity

Mitsuhiro Nakao^*

^*Corresponding author for this work

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

40 Citations (Scopus)

Abstract

We prove the existence of a strong anti-periodic solution for the quasilinear wave equation with viscosity u_tt - div{σ(|∇u|²)∇u} - Δu_t = f(x,t) in ΩXR under the Dirichlet boundary condition u(t)|_2Ω = 0, where Ω is a bounded domain in R^Nwith the boundary 2Ω and σ(v²) is a function like 1/ √1 + v².

Original language	English
Pages (from-to)	754-764
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	204
Issue number	3
DOIs	https://doi.org/10.1006/jmaa.1996.0465
Publication status	Published - 1996 Dec 15
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jmaa.1996.0465

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abstract = "We prove the existence of a strong anti-periodic solution for the quasilinear wave equation with viscosity utt - div{σ(|∇u|2)∇u} - Δut = f(x,t) in ΩXR under the Dirichlet boundary condition u(t)|2Ω = 0, where Ω is a bounded domain in RN with the boundary 2Ω and σ(v2) is a function like 1/ √1 + v2.",

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AB - We prove the existence of a strong anti-periodic solution for the quasilinear wave equation with viscosity utt - div{σ(|∇u|2)∇u} - Δut = f(x,t) in ΩXR under the Dirichlet boundary condition u(t)|2Ω = 0, where Ω is a bounded domain in RN with the boundary 2Ω and σ(v2) is a function like 1/ √1 + v2.

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Existence of an anti-periodic solution for the quasilinear wave equation with viscosity

Abstract

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