Wave-breaking phenomena and global existence for the generalized Fornberg-Whitham equation

[摘要] We consider the initial value problem for the generalized Fornberg-Whitham equation, which consists of p-order nonlinear advection term and nonlocal dispersion term. In the case of p = 2, we study sufficient conditions for blow-up of solutions and some relations to the Burgers equation. Also, for p >= 5, we show the global existence of the solutions with small initial data. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-01

[关键词] Generalized Fornberg-Whitham;equation;Burgers equation;Wave-breaking;Blow-up time;Global existence