【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.更多还原

【Abstract】 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.更多还原