非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 169-180.

非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破

欧阳柏平()

广州华商学院应用数学系广州 511300

收稿日期:2021-10-26 修回日期:2022-08-25 出版日期:2023-02-26 发布日期:2023-03-07
作者简介:欧阳柏平, E-mail: oytengfei79@tom.com
基金资助:
广东省普通高校自然科学重点项目(2019KZDXM042);广东省普通高校创新团队项目(2020WCXTD008);广州华商学院校内项目(2020HSDS01);广州华商学院校内项目(2021HSKT01)

Blow-up of Solutions to the Euler-Poisson-Darboux-Tricomi Equation with a Nonlinear Memory Term

Ouyang Baiping()

Department of Apllied Mathematics, Guangzhou Huashang College, Guangzhou 511300

Received:2021-10-26 Revised:2022-08-25 Online:2023-02-26 Published:2023-03-07
Supported by:
Key Projects of Universities in Guangdong Province (NATURAL SCIENCE)(2019KZDXM042);Innovation Team Project in Colleges and Universities of Guangdong Province(2020WCXTD008);Science Foundation of Guangzhou Huashang College(2020HSDS01);Science Foundation of Guangzhou Huashang College(2021HSKT01)

摘要/Abstract

摘要：

研究了具有非线性记忆项的Euler-Poisson-Darboux-Tricomi方程在次临界情况下解的爆破现象. 利用泛函分析方法结合修正的Bessel方程推出了其柯西问题解的迭代框架和第一下界, 然后通过迭代技巧, 获得了其解的全局非存在性以及解的生命跨度上界估计.

关键词: 非线性记忆项, Euler-Poisson-Darboux-Tricomi方程, 爆破

Abstract:

Blow-up phenomenon of solutions to the Euler-Poisson-Darboux-Tricomi equation with a nonlinear memory term in the subcritical case is studied. By using functional methods associated with a modified Bessel equation, an iteration frame and the first lower bound are derived. Then, nonexistence of global solutions to the Cauchy problem for the Euler-Poisson-Darboux-Tricomi equation and an upper bound estimate of solutions for the lifespan are obtained via the iteration technique.

Key words: Nonlinear memory term, Euler-Poisson-Darboux-Tricomi equation, Blow-up

中图分类号:

O175.2

欧阳柏平. 非线性记忆项的Euler-Poisson-Darboux-Tricomi方程解的爆破[J]. 数学物理学报, 2023, 43(1): 169-180.

Ouyang Baiping. Blow-up of Solutions to the Euler-Poisson-Darboux-Tricomi Equation with a Nonlinear Memory Term[J]. Acta mathematica scientia,Series A, 2023, 43(1): 169-180.

参考文献 24

[1]	D'ambrosio L, Lucente S. Nonlinear Liouville theorems for Grushin and Tricomi operators. J Differential Equations, 2003, 193(2): 511-541 doi: 10.1016/S0022-0396(03)00138-4
[2]	Yagdjian K. A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain. J Differential Equations, 2004, 206(1): 227-252 doi: 10.1016/j.jde.2004.07.028
[3]	Yagdjian K. Global existence for the $n$ -dimensional semilinear Tricomi-type equations. Comm Partial Differential Equations, 2006, 31(6): 907-944 doi: 10.1080/03605300500361511
[4]	Sun Y Q. Sharp lifespan estimates for subcritical generalized semilinear Tricomi equations. Math Meth Appl Sci, 2021, 44(13): 10239-10251 doi: 10.1002/mma.7402
[5]	Lin J Y, Tu Z H. Lifespan of semilinear generalized Tricomi equation with Strauss type exponent. Preprint, arXiv:1903.11351v2(2019)
[6]	He D Y, Witt I, Yin H C. On the global solution problem for semilinear generalized Tricomi equations, I. Calc Var, 2017, 56(2): Article 21 doi: 10.1007/s00526-017-1125-9
[7]	He D Y, Witt I, Yin H C. On semilinear Tricomi equations in one space dimension. Preprint, arXiv:1810. 12748(2018)
[8]	He D Y, Witt I, Yin H C. On semilinear Tricomi equations with critical exponents or in two space dimensions. J Differential Equations, 2017, 263(12): 8102-8137 doi: 10.1016/j.jde.2017.08.033
[9]	He D Y, Witt I, Yin H C. On the Strauss index of semilinear Tricomi equation. Commun Pure Appl Anal, 2020, 19(10): 4817-4838
[10]	Chen W H, Lucente S, Palmieri A. Nonexistence of global solutions for generalized Tricomi equations with combined nonlinearity. Nonlinear Anal Real World Appl, 2021, 61: 103354 doi: 10.1016/j.nonrwa.2021.103354
[11]	Palmieri A. Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime. Z Angew Math Phys, 2021, 72: Article 64 doi: 10.1007/s00033-021-01494-x
[12]	Palmieri A. On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity. Preprint, arXiv:2105.09879(2021)
[13]	Chen W H. Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms. Nonlinear Anal, 2021, 202: 112160 doi: 10.1016/j.na.2020.112160
[14]	Chen W H, Reissig M. Blow-up of solutions to Nakao's problem via an iteration argument. J Differential Equations, 2021, 275: 733-756 doi: 10.1016/j.jde.2020.11.009
[15]	Chen W H, Palmieri A. Nonexistence of global solutions for the semilinear Moore-Gibson-Thompson equation in the conservative case. Discrete Contin Dyn Syst, 2020, 40: 5513-5540 doi: 10.3934/dcds.2020236
[16]	Chen W H, Palmieri A. Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part. Z Angew Math Phys, 2019, 70(2): Article 67 doi: 10.1007/s00033-019-1112-4
[17]	Chen W H, Ikehata R. The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case. J Differential Equations, 2021, 292: 176-219 doi: 10.1016/j.jde.2021.05.011
[18]	欧阳柏平, 肖胜中. 具有非线性记忆项的半线性双波动方程解的全局非存在性. 数学物理学报, 2021, 41A(5): 1372-1381
	Ouyang B P, Xiao S Z. Nonexistence of global solutions for a semilinear Double-Wave equation with a nonlinear memory term. Acta Mathematica Scientia, 2021, 41A(5): 1372-1381
[19]	Lai N A, Takamura H, Wakasa K. Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent. J Differential Equations, 2017, 263: 5377-5394 doi: 10.1016/j.jde.2017.06.017
[20]	Palmieri A, Takamura A. Blow-up for a weekly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities. Nonlinear Anal, 2019, 187: 467-492 doi: 10.1016/j.na.2019.06.016
[21]	Yordanov B T, Zhang Q S. Finite time blow up for critical wave equations in high dimensions. J Funct Anal, 2006, 231(2): 361-374 doi: 10.1016/j.jfa.2005.03.012
[22]	Lai N A, Takamura H. Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture. Differ Integral Equ, 2019, 32: 37-48
[23]	Olver F W J, Lozier D W, Boisvert R F, Clark C W. NIST Handbook of Mathematical Functions. New York: Cambridge University Press, 2010
[24]	Palmieri A, Reissig M. A competition between Fujita and Strauss type exponents for blow-up of semi-linear wave equations with scale-invariant damping and mass. J Differ Equ, 2019, 266(2/3): 1176-1220 doi: 10.1016/j.jde.2018.07.061

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