✦ LIBER ✦
One application of Floquet's theory to Lp–Lq estimates for hyperbolic equations with very fast oscillations
✍ Scribed by Michael Reissig; Karen Yagdjian
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 140 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we consider the strictly hyperbolic equation u RR ! (t)b(t) u"0. The coe$cient consists of an increasing function " (t) and a non-constant periodic function b"b(t). We study the question for the in#uence of these parts on ¸N}¸O decay estimates for the solution of the Cauchy problem. A fairly wide class of equations will be described for which the in#uence of the oscillating part dominates. This implies, on the one hand, that there exist no ¸N}¸O decay estimates and, on the other hand, that the energy estimate from Gronwall's inequality is near to an optimal one.