摘要
针对一类具有强阻尼项的高阶Kirchhoff型方程的初边值问题,首先引入了几个重要的泛函和集合,并给出了整体弱解的定义。然后通过两个引理分析了整体弱解的性质,并且使用Galerkin方法构造了高阶Kirchhoff型方程的近似解。最后利用一些先验估计式,分析了近似解在不同范数下的有界性和收敛性,证明了这些近似解的极限就是高阶Kirchhoff型方程的整体弱解。
In this paper, the initial boundary value of the high order Kirchhoff type equation was studied. Firstly, we introduced some important functional and sets, defined the global weak solution, and analyzed the property of the global weak solutions through two lemmas. Then the approximate solutions of the higher order Kirchhoff type equation were constructed. Finally, the bounded property of the approximate solutions was analyzed by some priori estimates in different norm, and the convergence of the approximate solutions was discussed. It is proved that the limit of the approximate solutions is a global weak solution of the higher order Kirchhoff type equation.
出处
《淮南师范学院学报》
2016年第5期96-99,共4页
Journal of Huainan Normal University
基金
安徽省自然科学研究面上项目"分数阶微分发展系统的可控性研究"(1508085MA10)
宿州学院优秀青年人才支持计划重点项目"阻尼项和多个非线性源项共同作用下的波动方程整体解的存在性与不存在性问题"(2016XQNRL003)
