# American Institute of Mathematical Sciences

March  2020, 28(1): 15-25. doi: 10.3934/era.2020002

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

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

* Corresponding author: Byungsoo Moon

Received  September 2019 Revised  October 2019 Published  March 2020

Fund Project: The first author is supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03031180). The second author is supported by Incheon National University Research Grant in 2017.

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.

Citation: Guenbo Hwang, Byungsoo Moon. Global existence and propagation speed for a Degasperis-Procesi equation with both dissipation and dispersion. Electronic Research Archive, 2020, 28 (1) : 15-25. doi: 10.3934/era.2020002
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