Global existence and propagation speed for a Degasperis-Procesi equation with both dissipation and dispersion

Guenbo Hwang; Byungsoo Moon; Guenbo Hwang; Byungsoo Moon

doi:10.3934/era.2020002

Electronic Research Archive

2020, Volume 28, Issue 1: 15-25. doi: 10.3934/era.2020002

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Global existence and propagation speed for a Degasperis-Procesi equation with both dissipation and dispersion

Guenbo Hwang ^{1
,},
Byungsoo Moon ^{2
,
,}

1.
Department of Mathematics, Daegu University, Gyeongsan, Gyeongbuk 38453, Republic of Korea
2.
Department of Mathematics, Incheon National University, Incheon 22012, Republic of Korea

Received: 01 September 2019 Revised: 01 October 2019
Primary: 35B44, 35L05; Secondary: 37K10

In this paper, we consider the dissipative Degasperis-Procesi equation with arbitrary dispersion coefficient and compactly supported initial data. We establish the simple condition on the initial data which lead to guarantee that the solution exists globally. We also investigate the propagation speed for the equation under the initial data is compactly supported.
- Dissipative Degasperis-Procesi equation,
- blow-up,
- global solution,
- propagation speed
Citation: Guenbo Hwang, Byungsoo Moon. Global existence and propagation speed for a Degasperis-Procesi equation with both dissipation and dispersion[J]. Electronic Research Archive, 2020, 28(1): 15-25. doi: 10.3934/era.2020002

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Abstract

In this paper, we consider the dissipative Degasperis-Procesi equation with arbitrary dispersion coefficient and compactly supported initial data. We establish the simple condition on the initial data which lead to guarantee that the solution exists globally. We also investigate the propagation speed for the equation under the initial data is compactly supported.

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