Small data global existence for the semilinear wave equation with space-time dependent damping

Abstract

In this paper we consider the critical exponent problem for the semilinear wave equation with space-time dependent damping. When the damping is effective, it is expected that the critical exponent agrees with that of only space dependent coefficient case. We shall prove that there exists a unique global solution for small data if the power of nonlinearity is larger than the expected exponent. Moreover, we do not assume that the data are compactly supported. However, it is still open whether there exists a blow-up solution if the power of nonlinearity is smaller than the expected exponent.

Cited by in corpus (10)

• From $p_0(n)$ to $p_0(n+2)$
• The Threshold between Effective and Noneffective Damping for Semilinear Waves
• A note on the lifespan of solutions to the semilinear damped wave equation
• Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients
• Critical exponent for the semilinear wave equations with a damping increasing in the far field
• Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data
• Blow-up of solutions to the one-dimensional semilinear wave equation with damping depending on time and space variables
• A modified test function method for damped waves
• Critical exponent and sharp lifespan estimates for semilinear third-order evolution equations
• Blow up of solutions for semilinear wave equations with noneffective damping