Open AccessBlow-up of solutions to the coupled Tricomi equations with derivative type nonlinearities
Author(s) -
Jiangyan Yao,
Sen Ming,
Wei Han,
Xiuqing Zhang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022694
Subject(s) - mathematics , conjecture , derivative (finance) , type (biology) , cauchy distribution , argument (complex analysis) , function (biology) , pure mathematics , mathematical analysis , ecology , biochemistry , chemistry , evolutionary biology , financial economics , economics , biology
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.