Global Weak Solutions for the Weakly Dissipative Dullin-Gottwald-Holm Equation

Li, Shiyu (2021) Global Weak Solutions for the Weakly Dissipative Dullin-Gottwald-Holm Equation. Journal of Advances in Mathematics and Computer Science, 36 (9). pp. 91-108. ISSN 2456-9968

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Official URL: https://doi.org/10.9734/jamcs/2021/v36i930406

Abstract

In this paper, we are concerned with the existence and uniqueness of global weak solutions for the weakly dissipative Dullin-Gottwald-Holm equation describing the unidirectional propagation of surface waves in shallow water regime:
ut − α2uxxt + c0ux + 3uux + γuxxx + λ(u − α2uxx) = α2(2uxuxx + uuxxx).
Our main conclusion is that on c0 = − γ/α2 and λ ≥ 0, if the initial data satisfies certain sign conditions, then we show that the equation has corresponding strong solution which exists globally in time, finally we demonstrate the existence and uniqueness of global weak solutions to the equation.

Item Type:	Article
Subjects:	Afro Asian Library > Mathematical Science
Depositing User:	Unnamed user with email support@afroasianlibrary.com
Date Deposited:	21 Mar 2023 07:14
Last Modified:	29 Jul 2024 09:49
URI:	http://classical.academiceprints.com/id/eprint/80

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