arXiv Analytics

Sign in

arXiv:1810.03780 [math.AP]AbstractReferencesReviewsResources

The lifespan of solutions of semilinear wave equations with the scale invariant damping in one space dimension

Masakazu Kato, Hiroyuki Takamura, Kyouhei Wakasa

Published 2018-10-09Version 1

The critical constant of time-decaying damping in the scale invari- ant case is recently conjectured. It also has been expected that the lifespan estimate is the same as associated semilinear heat equations if the constant is in "heat-like" domain. In this paper, we point out that this is not true if the total integral of the sum of initial position and speed vanishes. In such a case, we have a new type of the lifespan estimates which is closely related to the non-damped case in shifted space dimensions.

Comments: 20 pages
Categories: math.AP
Subjects: 35L71, 35B44
Related articles: Most relevant | Search more
arXiv:1701.03232 [math.AP] (Published 2017-01-12)
Blow-up for semilinear wave equations with the scale invariant damping and super Fujita exponent
arXiv:1804.11073 [math.AP] (Published 2018-04-30)
Wave-like blow-up for semilinear wave equations with scattering damping and negative mass
arXiv:2103.08156 [math.AP] (Published 2021-03-15)
The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension

Links

Toolbox