Blow-up of solutions to the coupled Tricomi equations with derivative type nonlinearities

被引：0

作者：

Yao, Jiangyan ^{[1
]}

Ming, Sen ^{[2
]}

Han, Wei ^{[2
]}

Zhang, Xiuqing ^{[3
]}

机构：

[1] North Univ China, Data Sci & Technol, Taiyuan 030051, Peoples R China

[2] North Univ China, Dept Math, Taiyuan 030051, Peoples R China

[3] North Univ China, Dept Phys, Taiyuan 030051, Peoples R China

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 07期

关键词：

coupled Tricomi equations; derivative type nonlinearities; test function method; iteration method; blow-up; lifespan estimates; SEMILINEAR WAVE-EQUATIONS; GLOBAL EXISTENCE; LIFE-SPAN; REGULARITY;

D O I：

10.3934/math.2022694

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with blow-up results of solutions to coupled system of the Tricomi equations with derivative type nonlinearities. Upper bound lifespan estimates of solutions to the Cauchy problem with small initial values are derived by using the test function method (see the proof of Theorem 1.1) and iteration argument (see the proof of Theorem 1.2), respectively. Our main new contribution is that lifespan estimates of solutions to the problem in the sub-critical and critical cases which are connected with the Glassey conjecture are established. To the best knowledge of authors, the results in Theorems 1.1 and 1.2 are new.

引用

页码：12514 / 12535

页数：22

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