歐陽柏平

摘 要：考慮了一類具有導(dǎo)數(shù)型非線性記憶項(xiàng)的廣義Tricomi方程解的爆破問題。通過引入含時(shí)泛函和修正貝塞爾方程推出了解的迭代框架和第一下界；運(yùn)用迭代方法證明了在次臨界情況下解的全局非存在性和生命跨度上界估計(jì)。同時(shí)，得到了導(dǎo)數(shù)型非線性記憶項(xiàng)對(duì)廣義Tricomi方程解的非局部影響。

關(guān)鍵詞：導(dǎo)數(shù)型非線性記憶項(xiàng)；廣義Tricomi方程；爆破；生命跨度

中圖分類號(hào)：O175.2

文獻(xiàn)標(biāo)志碼：A

1 主要結(jié)果

2 主要結(jié)論的證明

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（責(zé)任編輯：于慧梅）

Blow-Up of Solutions to a Generalized Tricomi Equation with?a Nonlinear Memory Term of Derivative Type

OUYANG Baiping*

（Guangzhou Huashang College， Guangzhou 511300， China）

Abstract：In this research blow-up of solutions to a generalized Tricomi equation with a nonlinear memory term of derivative type is considered. By introducing time-dependent functionals and modified Bessel equations， an iterative frame and the first lower bound of solutions are derived. Then， application of iteration methods leads to proof of the nonexistence of global solutions and an upper bound estimate of solutions for the lifespan in subcritical case. Meanwhile， the nonlocal influence from the nonlinear memory term of derivative type on the solution of generalized Tricomi equation is obtained.

Key words：nonlinear memory term of derivative type; generalized Tricomi equation; blow-up; lifespan