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Global existence, asymptotic behaviour, and global non-existence of solutions for damped non-linear wave equations of Kirchhoff type in the whole space

✍ Scribed by Kosuke Ono

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 178 KB
Volume: 23
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(200004)23:6<535::aid-mma125>3.0.co;2-h

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✦ Synopsis

We study the global existence, asymptotic behaviour, and global non-existence (blow-up) of solutions for the damped non-linear wave equation of Kirchho! type in the whole space:

, and '0, with initial data u(x, 0)"u (x) and u R (x, 0)"u (x).

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