In this note, we prove the exact controllability for the semilinear wave equations in any space dimensions under the condition that the nonlinearity behaves like Ε½< < < < . ' o s ln s as s Βͺ Ο±.
Invariant Manifolds for Retarded Semilinear Wave Equations
β Scribed by M. Taboada; Y.C. You
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 858 KB
- Volume
- 114
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
## Abstract We study oscillatory properties of the solution to semilinear wave equation, assuming oscillatory terms in initial data have sufficiently small amplitude. The main result gives an a priori estimate of the remainder in the approximation by means of the method of __geometric optics__. The
We construct an invariant manifold of periodic orbits for a class of non-linear Schro dinger equations. Using standard ideas of the theory of center manifolds, we rederive the results of Soffer and Weinstein (Comm. Math. Phys. 133, 119 146 (1997); J. Differential Equations 98, 376 390 (1992)) on the