摘 要：研究了一類非線性記憶項(xiàng)的弱耦合半線性雙波動(dòng)系統(tǒng)解的爆破情況。 運(yùn)用測(cè)試函數(shù)和切片化方法，證明了其柯西問題在次臨界情況下解的全局非存在性。 同時(shí)，還得到了其解的生命跨度上界估計(jì)。

關(guān)鍵詞：非線性記憶項(xiàng)；弱耦合半線性雙波動(dòng)系統(tǒng)； 爆破

中圖分類號(hào)：O175.4

文獻(xiàn)標(biāo)志碼：A

參考文獻(xiàn)：

[1]AGEMI R， KUROKAWA Y H. TAKAMURA H. Critical curve for p-q systems of nonlinear wave equations in three space dimensions［J］. Journal of Differential Equations， 2000， 167（1）： 87-133.

［2］ ZHOU Y. Life span of classical solutions to ［J］. Chinese Annals Mathematics， Series B， 1992， 13： 230-243.

［3］ LIU Y， LI Y F， SHI J C. Estimates for the linear viscoelastic damped wave equation on the Heisenberg group［J］. Journal of Differential Equations， 2021， 285： 663-685.

［4］ YORDANOV B T， ZHANG Q S. Finite time blow up for critical wave equations in high dimensions［J］. Journal of Functional Analysis， 2006， 231 （2）： 361-374.

［5］ CHEN W H， PALMIERI A. Blow-up result for a semilinear wave equation with a nonlinear memory term// Cicognani M， Del Santo D， Parmeggiani A， Reissig M. Anomalies in Partial Differential Equations. Switzerland： Springer， 2021： 77-97.

［6］ CHEN W H. Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms［J］. Nonlinear Analysis， 2021， 202： 112160.

［7］ CHEN W H， REISSIG M. Blow-up of solutions to Nakao's problem via an iteration argument［J］. Journal of Differential Equations， 2021， 275： 733-756.

［8］ CHEN W H， PALMIERI A. Nonexistence of global solutions for the semilinear Moore-Gibson-Thompson equation in the conservative case［J］. Discrete and Continuous Dynamical Systems， 2020， 40： 5513-5540.

［9］ 歐陽柏平，肖勝中. 具有非線性項(xiàng)的弱耦合半線性Moore-Gibson-Thompson系統(tǒng)解的全局非存在性［J/OL］. 貴州大學(xué)學(xué)報(bào)（自然科學(xué)版）： 1-9［2021-10-21］. http：//kns.cnki.net/kcms/detail/52.5002.N.20210915.1740.002.html.

［10］LAI N A， TAKAMURA H. Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture［J］. Differential Integral Equations， 2019， 32： 37-48.

（責(zé)任編輯：于慧梅）

Blow-up Analysis on Solutions to a Weakly Coupled Semilinear

Double-wave System with Nonlinear Memory Terms

OUYANG Baiping*

（Guangzhou Huashang College， Guangzhou 511300， China）

Abstract：

Blow-up of solutions to a class of weakly coupled semilinear double-wave system with nonlinear memory terms is studied. By employing test functions and slicing methods， nonexistence of global solutions to the Cauchy problem for the semilinear double-wave system in the subcritical case is proved. Also， the upper bound estimate of the lifespan of solutions is obtained.

Key words：

nonlinear memory term; weakly coupled semilinear double-wave system; blow-up

收稿日期：2021-10-21

基金項(xiàng)目：廣東省普通高校創(chuàng)新團(tuán)隊(duì)資助項(xiàng)目（2020WCXTD008）；廣州華商學(xué)院校內(nèi)資助項(xiàng)目（2020HSDS01，2021HSKT01）

作者簡介：歐陽柏平（1979—），男，講師，碩士，研究方向：偏微分方程，E-mail：oytengfei79@163.com.

通訊作者：歐陽柏平，E-mail：oytengfei79@163.com.