Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity

Abstract

In our previous two works, we studied the blow-up and lifespan estimates for damped wave equations with a power nonlinearity of the solution or its derivative, with scattering damping independently. In this work, we are devoted to establishing a similar result for a combined nonlinearity. Comparing to the result of wave equation without damping, one can say that the scattering damping has no influence.

19 pages

References in corpus (7)

• Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent
• Blow-up for semilinear damped wave equations with sub-Strauss exponent in the scattering case
• Fujita versus Strauss - a never ending story
• A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent
• Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity
• The sharp estimate of the lifespan for the semilinear wave equation with time-dependent damping
• Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey conjecture

Cited by in corpus (12)

• Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity
• Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities
• A blow-up result for the semilinear Moore-Gibson-Thompson equation with nonlinearity of derivative type in the conservative case
• 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
• Blow-up for wave equation with the scale-invariant damping and combined nonlinearities
• New blow-up result for the weakly coupled wave equations with a scale-invariant damping and time derivative nonlinearity
• Blow up for small-amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds
• Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds