Blow up for the wave equation with a nonlinear dissipation of cubic convolution type in ℝN

Nasser Eddine Tatar

doi:10.1016/S0096-3003(02)00936-0

Blow up for the wave equation with a nonlinear dissipation 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

The solution of the wave equation with a nonlinear source of polynomial type and a nonlinear dissipation of nonlocal nature was shown to blow up in finite time. The dissipation was of cubic convolution type which involved a singular kernel. The proposed functional has the advantage that it allows for a larger class of initial data.

Original language	English
Pages (from-to)	759-771
Number of pages	13
Journal	Applied Mathematics and Computation
Volume	148
Issue number	3
DOIs	https://doi.org/10.1016/S0096-3003(02)00936-0
State	Published - 30 Jan 2004

Keywords

Blow up
Cubic convolution
Nonlocal dissipation
Singular kernel

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/S0096-3003(02)00936-0

Cite this

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title = "Blow up for the wave equation with a nonlinear dissipation of cubic convolution type in ℝN",

abstract = "The solution of the wave equation with a nonlinear source of polynomial type and a nonlinear dissipation of nonlocal nature was shown to blow up in finite time. The dissipation was of cubic convolution type which involved a singular kernel. The proposed functional has the advantage that it allows for a larger class of initial data.",

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AU - Tatar, Nasser Eddine

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N2 - The solution of the wave equation with a nonlinear source of polynomial type and a nonlinear dissipation of nonlocal nature was shown to blow up in finite time. The dissipation was of cubic convolution type which involved a singular kernel. The proposed functional has the advantage that it allows for a larger class of initial data.

AB - The solution of the wave equation with a nonlinear source of polynomial type and a nonlinear dissipation of nonlocal nature was shown to blow up in finite time. The dissipation was of cubic convolution type which involved a singular kernel. The proposed functional has the advantage that it allows for a larger class of initial data.

KW - Blow up

KW - Cubic convolution

KW - Nonlocal dissipation

KW - Singular kernel

UR - https://www.scopus.com/pages/publications/0242522205

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JF - Applied Mathematics and Computation

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