Blow-up of energy solutions for the semilinear generalized Tricomi equation with nonlinear memory term

Abstract

In this paper, we investigate blow-up conditions for the semilinear generalized Tricomi equation with a general nonlinear memory term in $ \mathbb{R}^n $ by using suitable functionals and employing iteration procedures. Particularly, a new combined effect from the relaxation function and the time-dependent coefficient is found.

Keywords

• wave equation
• semilinear hyperbolic equation
• generalized tricomi operator
• blow-up
• nonlinear memory term