弱耗散的广义Camassa-Holm方程的解及性质

The Existence of Solution and Property for Generalized Camassa-Holm Equation with Weak Dissipation

利用Kato定理方法证明了弱耗散的广义浅水波方程ut-uxxt-εuxx+g(u)x=2uxuxx+uuxxx关于初值问题的解的局部存在性,且发现解在初值以及g(u)给定条件下具有爆破性质.

The existence of local solution of generalized wave equation with weak dissipation ut-uxxt-εuxx＋g（u）x=2uxuxx＋uuxxx is obtained by using kato＇s existence theorem about the initial value problem . Moreover , the property of blow-up is founded with the initial profiles as well as under the special conditions.