Nonexistence of global solutions for generalized Tricomi equations with combined nonlinearity

TL;DR

This paper studies the blow-up behavior of solutions to a generalized Tricomi equation with combined nonlinearities, extending known blow-up regions and providing lifespan estimates using an iteration method.

Contribution

It introduces a new approach to analyze blow-up for generalized Tricomi equations with combined nonlinearities, enlarging the blow-up region compared to previous models.

Findings

Enlarged blow-up region for solutions.

Derived upper bounds for solution lifespan.

Established lower bounds for space averages of solutions.

Abstract

In the present paper, we investigate the blow-up dynamics for local solutions to the semilinear generalized Tricomi equation with combined nonlinearity. As a result, we enlarge the blow-up region in comparison to the ones for the corresponding semilinear models with either power nonlinearity or nonlinearity of derivative type. Our approach is based on an iteration argument to establish lower bound estimates for the space average of local solutions. Finally, we obtain upper bound estimates for the lifespan of local solutions as byproduct of our iteration argument.