Differential and Integral Equations

Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture

Ning-An Lai and Hiroyuki Takamura

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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's conjecture on nonlinear wave equations. We also study an upper bound of the lifespan for the scale invariant damping with the same method.

Article information

Source
Differential Integral Equations, Volume 32, Number 1/2 (2019), 37-48.

Dates
First available in Project Euclid: 11 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1544497285

Mathematical Reviews number (MathSciNet)
MR3909978

Zentralblatt MATH identifier
07031708

Subjects
Primary: 35L71: Semilinear second-order hyperbolic equations 35B44: Blow-up

Citation

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


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