Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities

Abstract

In this work we study the blow-up of solutions of a weakly coupled system of damped semilinear wave equations in the scattering case with power nonlinearities. We apply an iteration method to study both the subcritical case and the critical case. In the subcritical case our approach is based on lower bounds for the space averages of the components of local solutions. In the critical case we use the slicing method and a couple of auxiliary functions, recently introduced by Wakasa-Yordanov, to modify the definition of the functionals with the introduction of weight terms. In particular, we find as critical curve for the pair (p, q) of the exponents in the nonlinear terms the same one as for the weakly coupled system of semilinear wave equations with power nonlinearities.

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Cited by in corpus (10)

• A blow-up result for the semilinear Moore-Gibson-Thompson equation with nonlinearity of derivative type in the conservative case
• A note on a conjecture for the critical curve of a weakly coupled system of semilinear wave equations with scale-invariant lower order terms
• A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type
• Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
• Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case
• Nonexistence of global solutions for generalized Tricomi equations with combined nonlinearity
• Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms
• Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms
• Blow-up of solutions to Nakao's problem via an iteration argument
• Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime