Nonexistence of global solutions for generalized Tricomi equations with combined nonlinearity

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.

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Cited by in corpus (4)

• Blow-up and lifespan estimate for generalized Tricomi equations related to Glassey conjecture
• Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
• On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity
• Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type