一类具有导数型非线性记忆项和变系数耗散的广义Tricomi方程全局解的非存在性

Nonexistence of Global Solutions to a Class of Dissipative Generalized Tricomi Equations with Nonlinear Memory Terms of Derivative Type and Variable Coefficients

考虑一类具有导数型非线性记忆项和变系数耗散的广义Tricomi方程全局解的非存在性问题,通过构造能量泛函,利用Bessel方程和迭代技巧,给出次临界情形下其Cauchy问题能量解的爆破结果,并进一步给出导数型非线性记忆项对其Cauchy问题解的非局部影响及其解的生命跨度估计.

The author considered nonexistence of global solutions to a class of dissipative generalized Tricomi equations with nonlinear memory terms of derivative type and variable coefficients. By constructing energy functionals and using Bessel equations and iterative techniques, the author gave the result of blow-up of energy solutions to the Cauchy problem in the subcritical case. Furthermore, the author gave the nonlocal effect of nonlinear memory terms of derivative type on the solution of Cauchy problem and the estimation of the lifespan for the solutions.