## Abstract We present a global existence theorem for solutions of __u__^__tt__^ − ∂~__i__~__a__~__ik__~ (__x__)∂~__k__~__u__ + u~t~ = ƒ(__t__, __x__, __u__, __u__~__t__~, ∇__u__, ∇__u__~__t__~, ∇^2^__u__), __u__(__t__ = 0) = __u__^0^, __u__(=0)=__u__^1^, __u__(__t, x__), __t__ ⪖ 0, __x__ϵΩ.Ω equal
Dynamics of non-linear wave equations
✍ Scribed by Grozdena Todorova
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 118 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.563
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✦ Synopsis
Abstract
We present several stability/instability results for the ground‐state standing waves and high‐energy‐bound‐state standing waves for the NLKG, NLS and NLDW equations. At the end of the paper we present a number of open problems. Copyright © 2004 John Wiley & Sons, Ltd.
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