关键词: 导数型非线性记忆项, 变系数, 广义Tricomi方程, 爆破, 生命跨度

Abstract: 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.

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