关于2类四阶非线性方程的解的爆破  

The blow-up of solutions to two classes of nonlinear equations of four order

作　　者：官翠婷 尚亚东[1] GUAN Cui-ting;SHANG Ya-dong(School of Mathematics and Information Sciences,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2018年第2期23-26,共4页Journal of Guangzhou University:Natural Science Edition

基　　金：国家自然科学基金天元基金资助项目(11626070)

摘　　要：考察2类四阶非线性发展偏微分方程初边值问题,利用特征值问题对应的特征函数,结合Jensen不等式对2类四阶非线性方程构造了关于时间的常微分不等式.进而证明了问题的解在有限时间内会产生爆破现象,给出了有限时间内发生爆破的充分条件和爆破时间的上界估计,并给出相应的具体例子.The initial boundary value problems of two classes of four order nonlinear equations are investigated.Some ordinary differential inequalities with respect to time for two classes of nonlinear equations of four order are constructed by using the eigenfunctions corresponding to the eigenvalue problems and Jensen’s inequality. Then the solutions of these equations which give rise to blow up phenomena in finite time can be proved. Some sufficient conditions are added to nonlinear functions and the initial values are given. Under these conditions the solution will blow up. Several examples are also given after the theorems.

关 键 词：特征函数 非线性 高阶方程 爆破 

分 类 号：O175.29[理学—数学]