Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity

Abstract

In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow 'wave-like'. A Strauss type critical exponent is determined as the upper bound for the exponent in the nonlinearity in the main theorems. Two blow-up results are obtained for the sub-critical case and for the critical case, respectively. In both cases, an upper bound lifespan estimate is given.

arXiv comment23 pages

References in corpus (9)

• From $p_0(n)$ to $p_0(n+2)$
• The Threshold between Effective and Noneffective Damping for Semilinear Waves
• 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
• Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity
• Global existence of solutions for semi-linear wave equation with scale-invariant damping and mass in exponentially weighted spaces
• Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term

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• The semilinear Euler-Poisson-Darboux equation: a case of wave with critical dissipation
• 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 generalized Tricomi equations with combined nonlinearity
• Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part
• Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms
• A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime
• Blow-up for wave equation with the scale-invariant damping and combined nonlinearities
• Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime
• On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity
• A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term
• Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case
• Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass
• New blow-up result for the weakly coupled wave equations with a scale-invariant damping and time derivative nonlinearity
• Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds