Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case

Abstract

We study global existence of solutions to the Cauchy problem for the wave equation with time-dependent damping and a power nonlinearity in the overdamping case. We prove the global well-posedness for small data in the energy space for the whole energy-subcritical case. This result implies that small data blow-up does not occur in the overdamping case, different from the other cases, i.e. effective or non-effective damping.

arXiv comment15 pages, typos are corrected and the references are updated

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Cited by in corpus (6)

• Sharp lifespan estimates of blowup solutions to semilinear wave equations with time-dependent effective damping
• Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term
• Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass
• On the blow-up for critical semilinear wave equations with damping in the scattering case
• Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping
• Blow up of solutions for semilinear wave equations with noneffective damping