Differential and Integral Equations

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

Masakazu Kato, Hiroyuki Takamura, and Kyouhei Wakasa

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Abstract

The critical constant $\mu$ (see (1.1)) of time-decaying damping in the scale-invariant case is recently conjectured. It also has been expected that the lifespan estimate is the same as for the associated semilinear heat equations if the constant is in the “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.

Article information

Source
Differential Integral Equations, Volume 32, Number 11/12 (2019), 659-678.

Dates
First available in Project Euclid: 22 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1571731514

Mathematical Reviews number (MathSciNet)
MR4021258

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

Citation

Kato, Masakazu; Takamura, Hiroyuki; Wakasa, Kyouhei. The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension. Differential Integral Equations 32 (2019), no. 11/12, 659--678. https://projecteuclid.org/euclid.die/1571731514


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