On the Cauchy Problem for a Weakly Dissipative Periodic Two-Component Dullin-Gottwald-Holm System
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Haicui Lv, Yanli Wang, Jia Song
The local well-posedness of the weakly dissipative nonlinear shallow water wave equation is established. For different initial values, we obtain the global existence of the solution and the blow-up of the solution respectively. It is necessary to study the influence of dissipation term on the system solution. Due to the complexity of the equation itself, it is difficult to find a connection between each other. The abstract Cauhcy problem is the most significant application theme of the operator semi-group, so the two promote and grow together. The domain of the generator can be relaxed to the polynomial case without the need for dense and pre-solved estimates. This has broadly broadened its scope of application.
Cauchy problem, Weak dissipation, Equation