On the wave equation with a dissipation and a source of cubic convolution type in ℝN

Nasser Eddine Tatar

doi:10.1515/dema-2004-0306

On the wave equation with a dissipation and a source of cubic convolution type in ℝ^N

Nasser Eddine Tatar^*

^*Corresponding author for this work

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

3 Scopus citations

Abstract

We study the interaction between a dissipative term and a source term of cubic convolution type for the wave equation in ℝ^N. These terms have both the same form and involve convolutions with a singular kernel. The investigation will depend on the coefficient of the source term which is a function of the time variable. Some results on the boundedness of the solutions are proved. Moreover, we establish an asymptotic stability result.

Original language	English
Pages (from-to)	543-555
Number of pages	13
Journal	Demonstratio Mathematica
Volume	37
Issue number	3
DOIs	https://doi.org/10.1515/dema-2004-0306
State	Published - Jul 2004

Bibliographical note

Publisher Copyright:
© 2014 Warsaw University. All rights reserved.

Keywords

Asymptotic behavior
Cubic convolution
Nonlinear dissipation
Polynomial growth
Singular kernel

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1515/dema-2004-0306

Cite this

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