A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term

Abstract

In this paper, we investigate blow-up of solutions to semilinear wave equations with scale-invariant damping and nonlinear memory term in ${\mathbb{R}}^n$, which can be represented by the Riemann-Liouville fractional integral of order $1-\gamma$ with $\gamma \in (0,1)$. Our main interest is to study mixed influence from damping term and the memory kernel on blow-up conditions for the power of nonlinearity, by using test function method or generalized Kato's type lemma. We find a new competition, particularly for the small value of $\gamma$, on the blow-up range between the effective case and the non-effective case.

References in corpus (11)

• 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
• Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity
• A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent
• A global existence result for a semilinear wave equation with scale-invariant damping and mass in even space dimension
• Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type lemma
• The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions
• The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension
• Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms
• Weighted $L^2-L^2$ estimate for wave equation and its applications