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

Jiangyan Yao; Sen Ming; Wei Han; Xiuqing Zhang; Jiangyan Yao; Sen Ming; Wei Han; Xiuqing Zhang

doi:10.3934/math.2022694

AIMS Mathematics

2022, Volume 7, Issue 7: 12514-12535. doi: 10.3934/math.2022694

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Research article

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

1.
Data Science and Technology, North University of China, Taiyuan 030051, China
2.
Department of Mathematics, North University of China, Taiyuan 030051, China
3.
Department of Physics, North University of China, Taiyuan 030051, China

Received: 14 February 2022 Revised: 12 April 2022 Accepted: 15 April 2022 Published: 27 April 2022
MSC : 35L70, 58J45

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.
- coupled Tricomi equations,
- derivative type nonlinearities,
- test function method,
- iteration method,
- blow-up,
- lifespan estimates
Citation: Jiangyan Yao, Sen Ming, Wei Han, Xiuqing Zhang. Blow-up of solutions to the coupled Tricomi equations with derivative type nonlinearities[J]. AIMS Mathematics, 2022, 7(7): 12514-12535. doi: 10.3934/math.2022694

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Abstract

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.

References

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