导数型非线性记忆项下广义Tricomi方程解的爆破

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

考虑了一类具有导数型非线性记忆项的广义Tricomi方程解的爆破问题。通过引入含时泛函和修正贝塞尔方程推出了解的迭代框架和第一下界;运用迭代方法证明了在次临界情况下解的全局非存在性和生命跨度上界估计。同时,得到了导数型非线性记忆项对广义Tricomi方程解的非局部影响。

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.