中北大学学报（自然科学版）2024，Vol.45Issue(1)：36-43,8.DOI:10.3969/j.issn.1673-3193.2024.01.005
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
摘要
Abstract
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Key words
derivative nonlinearity/coupled Tricomi equations/Kato's lemma/iteration method/blow-up/lifespan分类
数理科学引用本文复制引用
王晓东,明森,韩伟,任翠..带导数非线性项的耦合Tricomi方程组解的破裂[J].中北大学学报（自然科学版）,2024,45(1):36-43,8.基金项目
山西省基础研究计划资助项目(20210302123045,20210302123021,20210302123182) （20210302123045,20210302123021,20210302123182）
中北大学科研创新团队支持计划资助项目(TD201901) （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 （）
