Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey conjecture
arXiv:1711.07591
Abstract
This work is devoted to the nonexistence of global-in-time energy solutions of nonlinear wave equation of derivative type with weak time-dependent damping in the scattering and scale invariant range. By introducing some multipliers to absorb the damping term, we succeed in establishing the same upper bound of the lifespan for the scattering damping as the non-damped case, which is a part of so-called Glassey conjecture on nonlinear wave equations. We also study an upper bound of the lifespan for the scale invariant damping with the same method.
13 pages. In the second version, the trivial mistake in the statement of theorems is modified and the regularity in the definition of the solution is corrected