带导数非线性项的耦合Tricomi方程组解的破裂  

Blow‑Up of Solutions for the Coupled System of Tricomi Equations with Derivative Nonlinearity

作　　者：王晓东[1] 明森 韩伟[1] 任翠 WANG Xiaodong;MING Sen;HAN Wei;REN Cui(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2024年第1期36-43,共8页Journal of North University of China(Natural Science Edition)

基　　金：山西省基础研究计划资助项目(20210302123045,20210302123021,20210302123182);中北大学科研创新团队支持计划资助项目(TD201901);山西省高等学校优秀青年学术带头人支持计划资助项目。

摘　　要：在空间维数n≥2时,研究带导数非线性项的耦合Tricomi方程组的小初值问题。通过定义问题的能量解并构造适当的检验函数,得到关于解的积分泛函的不等式。根据非线性项指数的范围将解的性态研究分为次临界情形及临界情形。在次临界情形利用改进的Kato引理,在临界情形利用迭代方法,证明了问题的解会在有限时间破裂。同时,在次临界情形得到幂次形式解的生命跨度的上界估计,在临界情形得到指数形式解的生命跨度的上界估计,推广了现有文献的结论。The small initial values problem of coupled Tricomi equations with derivative nonlinearity with space dimensional n≥2 is studied.By defining the energy solutions of the problem and constructing the adequate test function,the integral functional inequalities of solutions are obtained.According to the range of nonlinearities exponents,the research process is divided into the sub-critical case and critical cases.By using the improved Kato’s lemma in the sub-critical case and iterative method in the critical case,it shows that solutions to the problem blow up in finite time.Meanwhile,the upper bound lifespan estimates in power form for the sub-critical case and exponential form for the critical case are obtained,which general‐izes the conclusions of existing literatures.

关 键 词：导数非线性项 耦合Tricomi方程 Kato引理 迭代方法 破裂 生命跨度 

分 类 号：O175.29[理学—数学]