Explicit decay rates for a generalized Boussinesq-Burgers system

作者：Zhu, Neng; Liu, Zhengrong; Wang, Fang; Zhao, Kun^*

来源：Applied Mathematics Letters, 2020, 100: 106054.

DOI：10.1016/j.aml.2019.106054

• Boussinesq-Burgers system
• Cauchy problem
• Explicit decay rates

This paper is concerned with the long-time asymptotic behavior of classical solutions to the Cauchy problem for the generalized Boussinesq-Burgers system: @@@ {u(t) + (uw)(x) = epsilon u(xx), x is an element of R, t > 0, w(t) + (u(gamma) + w(2)/2)(x) = mu w(xx) + delta w(xxt), x is an element of R, t > 0, (u, w)(x, 0) = (u(0), w(0))(x), x is an element of R, @@@ where gamma >= 2, epsilon, mu and delta are positive constants. By utilizing time-weighted energy methods, we identify the explicit decay rates of classical solutions to the Cauchy problem under mild conditions on the initial data. This generalizes the previous result obtained in Zhu and Liu (2016) by extending the exponent gamma from a single value to the half real line.

• 单位
  南昌大学; 长沙理工大学