一类Kirchhoff型双曲方程在任意初始能量下的有限时刻爆破  

Finite time blow up for a Kirchhoff-type hyperbolic problem with arbitrary initial energy

作　　者：邵湘琨 唐国吉[1,2] SHAO Xiang-kun;TANG Guo-ji(School of Mathematics and Physics,Guangxi University for Nationalities,Guangxi 530006,China;Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis,Guangxi 530006,China)

机构地区：[1]广西民族大学数学与物理学院,广西南宁530006 [2]广西混杂计算与集成电路设计分析重点实验室,广西南宁530006

出　　处：《高校应用数学学报（A辑）》2021年第4期438-450,共13页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11961006);广西自然科学基金(2020GXNSFAA159100);广西研究生教育创新计划(YCSW2020136)。

摘　　要：研究一类带有分数次算子的Kirchhoff型双曲方程的有限时刻爆破问题.找到了一个与势阱深度无关的有限时刻爆破条件并估计了爆破时间上界,进一步,得到了解在任意高初始能量下的有限时刻爆破结果.文中的主要结果扩展了已有的一些爆破结果.In this paper,the finite time blow up of a Kirchhoff-type hyperbolic problem with fractional operator is investigated.A blow up condition independent of the depth of the potential well is found and the upper bound of the blow up time is given.Furthermore,the finite time blow up result of solutions with arbitrary high initial energy is obtained.The main results presented in this paper generalize the recent ones in the literature.

关 键 词：Kirchhoff双曲方程 有限时刻爆破 任意初始能量 

分 类 号：O175.27[理学—数学]