Infinite propagation speed and asymptotic behavior for a generalized fifth-order Camassa–Holm equation

ABSTRACT

In this paper we consider the Cauchy problem for a generalized fifth-order Camassa–Holm equation. The infinite propagation speed is proved in the following sense: the corresponding solution u(x, t) with compactly supported initial data $u_0(x)$ does not have compact support in its lifespan. Moreover, the asymptotic behaviors of the solution at infinity are considered when the initial data decays exponentially and algebraically, respectively.

KEYWORDS:

• Generalized fifth-order Camassa–Holm equation
• infinite propagation speed
• asymptotic behavior

AMS SUBJECT CLASSIFICATIONS:

• 35B40
• 35B30
• 35G25

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

L. Han was supported by the Fundamental Research Funds for the Central Universities [grant number 2015MS53].