Semi-linear Wave Equations with Effective Damping

The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b（t）〉 0 is effective, and in particular tb（t） →∞ as t →∞. The global existence of small energy...

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Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 34; no. 3; pp. 345 - 380
Main Authors D’Abbicco, Marcello, Lucente, Sandra, Reissig, Michael
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.05.2013
Department of Mathematics, University of Bari, Via E.Orabona 4, 70125 Bari, Italy%Faculty for Mathematics and Computer Science, Technical University Bergakademie Freiberg, Priiferstr.9,09596 Freiberg, Germany
Subjects
Applications of Mathematics
Cauchy问题
Mathematics
Mathematics and Statistics
UT斯达康
半线性波动方程
整体存在性
时间相关
空间维度
阻尼波动方程
阻尼项
Semi-linear equations
Global existence
Critical exponent
35L71
Damped wave equations
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ISSN0252-9599
1860-6261
DOI10.1007/s11401-013-0773-0

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Summary:The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b（t）〉 0 is effective, and in particular tb（t） →∞ as t →∞. The global existence of small energy data solutions for｜f（u）｜≈｜u｜^p in the supercritical case of p 〉 1＋ 2/n and p ≤n/n-2 for n ≥ 3 is proved.
Bibliography:Semi-linear equations; Damped wave equations; Critical exponent;Global existence
The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b（t）〉 0 is effective, and in particular tb（t） →∞ as t →∞. The global existence of small energy data solutions for｜f（u）｜≈｜u｜^p in the supercritical case of p 〉 1＋ 2/n and p ≤n/n-2 for n ≥ 3 is proved.
31-1329/O1
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-013-0773-0