We are concerned with the blowup phenomena of a dissipative Dullin–Gottwald–Holm equation which can describe unidirectional propagation of surface waves in a shallow water regime. A “local-in-space” blowup criterion is obtained by delicate analysis on the evolution of some linear combinations of the solution u and its derivative \(u_x\). The result is the improvement of E. Novruzov’s theorem on the dissipative Dullin–Gottwald–Holm equation with some special coefficients.

中文翻译：

---

耗散Dullin – Gottwald – Holm方程的“空间局部爆破”准则

我们关注耗散的Dullin – Gottwald – Holm方程的爆炸现象，该方程可描述浅水状态下表面波的单向传播。通过对解u及其导数\（u_x \）的一些线性组合的演化的精细分析，获得了“空间局部爆炸”准则。结果是改进了耗散Dullin – Gottwald – Holm方程的E. Novruzov定理，并带有一些特殊系数。