Existence of a solution of the wave equation with nonlinear damping and source terms

Vladimir Georgiev; Grozdena Todorova

doi:10.1006/jdeq.1994.1051

Existence of a solution of the wave equation with nonlinear damping and source terms

Vladimir Georgiev, Grozdena Todorova

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

479 Citations (Scopus)

Abstract

We study the nonlinear wave equation involving the nonlinear damping term u_t |u_t|^m-1 and a source term of type u |u|^p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.

Original language	English
Pages (from-to)	295-308
Number of pages	14
Journal	Journal of Differential Equations
Volume	109
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.1994.1051
Publication status	Published - 1994 Apr 15
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1006/jdeq.1994.1051

Cite this

@article{359516fe2c9c4091ae4ee5d4ce543e49,

title = "Existence of a solution of the wave equation with nonlinear damping and source terms",

abstract = "We study the nonlinear wave equation involving the nonlinear damping term ut |ut|m-1 and a source term of type u |u|p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.",

author = "Vladimir Georgiev and Grozdena Todorova",

year = "1994",

month = apr,

day = "15",

doi = "10.1006/jdeq.1994.1051",

language = "English",

volume = "109",

pages = "295--308",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Existence of a solution of the wave equation with nonlinear damping and source terms

AU - Georgiev, Vladimir

AU - Todorova, Grozdena

PY - 1994/4/15

Y1 - 1994/4/15

N2 - We study the nonlinear wave equation involving the nonlinear damping term ut |ut|m-1 and a source term of type u |u|p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.

AB - We study the nonlinear wave equation involving the nonlinear damping term ut |ut|m-1 and a source term of type u |u|p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.

UR - http://www.scopus.com/inward/record.url?scp=0000028946&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000028946&partnerID=8YFLogxK

U2 - 10.1006/jdeq.1994.1051

DO - 10.1006/jdeq.1994.1051

M3 - Article

AN - SCOPUS:0000028946

VL - 109

SP - 295

EP - 308

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -

Existence of a solution of the wave equation with nonlinear damping and source terms

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this