In this paper, we study the weakly dissipative asymptotically equivalent shallow water wave equations on the circle, which is called the weakly dissipative periodic b-family of equations. Under the effect of dissipation, we derive two blow-up criteria to this equation with certain initial data. When the parameters α, λ, and b belong to a suitable range, our present blow-up criteria improve and extend the previous relevant blow-up results.

中文翻译：

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弱耗散周期性 b 族方程组的爆炸问题

本文研究了圆上的弱耗散渐近等效浅水波动方程，称为弱耗散周期b族方程。在耗散的影响下，我们用某些初始数据推导出该方程的两个膨胀标准。当参数 α、λ 和 b 属于合适的范围时，我们目前的爆破标准改进和扩展了之前的相关爆破结果。