摘要
在狄利克雷边界和声学边界共同作用下,文章研究一类具有异号源项的Kirchhoff型方程的解的爆破问题,利用格林第一公式证明方程的能量泛函单调递减.引入一个特殊的泛函,并在初始能量为负的条件下,利用放缩的方法证明该泛函满足的两个不等式,利用该不等式证明方程的解必在有限时间内爆破.
This paper considers the blow up problem for the Kirchhoff type equation wit hdifferent source terms.The equation is associated with Dirichlet boundary conditions at one part and acoustic boundary condi-tions at another part, respectively.It is proved that the energy functional is monotonically decreasing by Green′sfirst formula.And then, a special functional is introduced, we prove two inequalities for the functional by the method of shrinking. Finally, it is obtained that the solutions of the equation blow up in a finite time.
作者
晋守博
JIN Shoubo(School of Mathematics and Statistics, Suzhou University, 234000, Suzhou, Anhui, Chin)
出处
《淮北师范大学学报(自然科学版)》
CAS
2018年第2期1-5,共5页
Journal of Huaibei Normal University:Natural Sciences
基金
安徽省高校自然科学研究重点项目(KJ2017A442)
宿州学院重点研究项目(2016yzd06)
宿州学院优秀青年人才支持计划项目(2016XQNRL003)