The Blow-Up of Solutions to the Cauchy Problem of Semilinear Tricomi Equations with Damping and Mass Terms

Abstract

This paper is related to the blow-up results of solutions to the Cauchy problem of semilinear generalized Tricomi equations, which contain a scale-invariant damping term and a mass term. The nonlinear term is of the power type in the case of a single equation, and of the power type and combined type in the case of a coupled system. The upper bound estimate for the lifespan of the solution to the problem with a power-type nonlinear term is obtained by applying the test function method. The lifespan estimates of solutions to the coupled system with power nonlinearities and combined nonlinearities are derived using the iteration method. It is worth pointing out that the time-dependent coefficients of the damping term and mass term determine competition between the Strauss critical exponent and Fujita critical exponent.