Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent

Ning An Lai; Hiroyuki Takamura; Kyouhei Wakasa

doi:10.1016/j.jde.2017.06.017

Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent

Ning An Lai, Hiroyuki Takamura, Kyouhei Wakasa

Research output: Contribution to journal › Article › peer-review

58 Citations (Scopus)

Abstract

The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case of non-effective damping. In this paper we extend his result in two aspects by showing that: (I) the blow-up will happen for bigger exponent, which is closely related to the Strauss exponent, the critical number for non-damped semilinear wave equations; (II) such a blow-up result is established for a wider range of the constant than the known non-effective one in the damping term.

Original language	English
Pages (from-to)	5377-5394
Number of pages	18
Journal	Journal of Differential Equations
Volume	263
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2017.06.017
Publication status	Published - 2017 Nov 5
Externally published	Yes

Keywords

Blow-up
Damped wave equation
Semilinear

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2017.06.017

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title = "Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent",

abstract = "The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case of non-effective damping. In this paper we extend his result in two aspects by showing that: (I) the blow-up will happen for bigger exponent, which is closely related to the Strauss exponent, the critical number for non-damped semilinear wave equations; (II) such a blow-up result is established for a wider range of the constant than the known non-effective one in the damping term.",

keywords = "Blow-up, Damped wave equation, Semilinear",

author = "Lai, {Ning An} and Hiroyuki Takamura and Kyouhei Wakasa",

note = "Funding Information: The first author is partially supported by NSFC (11501273), high level talent project of Lishui City (2016RC25), the Scientific Research Foundation of the First-Class Discipline of Zhejiang Province (B) (201601), the key laboratory of Zhejiang Province (2016E10007). The second author is partially supported by the Grant-in-Aid for Scientific Research (C) (No. 15K04964), Japan Society for the Promotion of Science, and Special Research Expenses in FY2016, General Topics (No. B21), Future University Hakodate. Publisher Copyright: {\textcopyright} 2017 The Authors",

year = "2017",

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doi = "10.1016/j.jde.2017.06.017",

language = "English",

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AU - Lai, Ning An

AU - Takamura, Hiroyuki

AU - Wakasa, Kyouhei

N1 - Funding Information: The first author is partially supported by NSFC (11501273), high level talent project of Lishui City (2016RC25), the Scientific Research Foundation of the First-Class Discipline of Zhejiang Province (B) (201601), the key laboratory of Zhejiang Province (2016E10007). The second author is partially supported by the Grant-in-Aid for Scientific Research (C) (No. 15K04964), Japan Society for the Promotion of Science, and Special Research Expenses in FY2016, General Topics (No. B21), Future University Hakodate. Publisher Copyright: © 2017 The Authors

PY - 2017/11/5

Y1 - 2017/11/5

N2 - The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case of non-effective damping. In this paper we extend his result in two aspects by showing that: (I) the blow-up will happen for bigger exponent, which is closely related to the Strauss exponent, the critical number for non-damped semilinear wave equations; (II) such a blow-up result is established for a wider range of the constant than the known non-effective one in the damping term.

AB - The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case of non-effective damping. In this paper we extend his result in two aspects by showing that: (I) the blow-up will happen for bigger exponent, which is closely related to the Strauss exponent, the critical number for non-damped semilinear wave equations; (II) such a blow-up result is established for a wider range of the constant than the known non-effective one in the damping term.

KW - Blow-up

KW - Damped wave equation

KW - Semilinear

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JF - Journal of Differential Equations

SN - 0022-0396

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Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent

Abstract

Keywords

ASJC Scopus subject areas

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