On solutions of the wave equation with a sublinear dissipative term

Mitsuhiro Nakao

doi:10.1016/0022-0396(87)90118-5

On solutions of the wave equation with a sublinear dissipative term

Mitsuhiro Nakao^*

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

The existence of periodic solution and a certain decay property for the nonlinear dissipative wave equation u_tt - Δu + σ(u_t) = f in R × Ω (or R⁺ × Ω) with the boundary condition u|∂Ω = 0 are proved, where Ω is a bounded domain in Rⁿ and σ(v) is a sublinear function, say, σ(v) = k₀|v|^-rv, k₀ >0, 0<r<1.

Original language	English
Pages (from-to)	204-215
Number of pages	12
Journal	Journal of Differential Equations
Volume	69
Issue number	2
DOIs	https://doi.org/10.1016/0022-0396(87)90118-5
Publication status	Published - 1987 Sept 15
Externally published	Yes

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/0022-0396(87)90118-5

Cite this

@article{509471758f684498abcf6784b04ec64d,

title = "On solutions of the wave equation with a sublinear dissipative term",

abstract = "The existence of periodic solution and a certain decay property for the nonlinear dissipative wave equation utt - Δu + σ(ut) = f in R × Ω (or R+ × Ω) with the boundary condition u|∂Ω = 0 are proved, where Ω is a bounded domain in Rn and σ(v) is a sublinear function, say, σ(v) = k0|v|-rv, k0 >0, 0",

author = "Mitsuhiro Nakao",

year = "1987",

month = sep,

day = "15",

doi = "10.1016/0022-0396(87)90118-5",

language = "English",

volume = "69",

pages = "204--215",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - On solutions of the wave equation with a sublinear dissipative term

AU - Nakao, Mitsuhiro

PY - 1987/9/15

Y1 - 1987/9/15

N2 - The existence of periodic solution and a certain decay property for the nonlinear dissipative wave equation utt - Δu + σ(ut) = f in R × Ω (or R+ × Ω) with the boundary condition u|∂Ω = 0 are proved, where Ω is a bounded domain in Rn and σ(v) is a sublinear function, say, σ(v) = k0|v|-rv, k0 >0, 0

AB - The existence of periodic solution and a certain decay property for the nonlinear dissipative wave equation utt - Δu + σ(ut) = f in R × Ω (or R+ × Ω) with the boundary condition u|∂Ω = 0 are proved, where Ω is a bounded domain in Rn and σ(v) is a sublinear function, say, σ(v) = k0|v|-rv, k0 >0, 0

UR - http://www.scopus.com/inward/record.url?scp=38249035301&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249035301&partnerID=8YFLogxK

U2 - 10.1016/0022-0396(87)90118-5

DO - 10.1016/0022-0396(87)90118-5

M3 - Article

AN - SCOPUS:38249035301

SN - 0022-0396

VL - 69

SP - 204

EP - 215

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

On solutions of the wave equation with a sublinear dissipative term

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this