Differential and Integral Equations
- Differential Integral Equations
- Volume 32, Number 1/2 (2019), 37-48.
Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture
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's conjecture on nonlinear wave equations. We also study an upper bound of the lifespan for the scale invariant damping with the same method.
Differential Integral Equations, Volume 32, Number 1/2 (2019), 37-48.
First available in Project Euclid: 11 December 2018
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L71: Semilinear second-order hyperbolic equations 35B44: Blow-up
Lai, Ning-An; Takamura, Hiroyuki. Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture. Differential Integral Equations 32 (2019), no. 1/2, 37--48. https://projecteuclid.org/euclid.die/1544497285