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November/December 2019 The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension
Masakazu Kato, Hiroyuki Takamura, Kyouhei Wakasa
Differential Integral Equations 32(11/12): 659-678 (November/December 2019).

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.

Citation

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Masakazu Kato. Hiroyuki Takamura. Kyouhei Wakasa. "The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension." Differential Integral Equations 32 (11/12) 659 - 678, November/December 2019.

Information

Published: November/December 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07144908
MathSciNet: MR4021258

Subjects:
Primary: 35B44, 35L71

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 11/12 • November/December 2019
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