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A remark on observability of the wave equation with moving boundary

Ammari K., Bchatnia A., El Mufti K.

Journal of Applied Analysis

2017

Vol. 23, nr 1

43--51

We deal with thewave equation with assigned moving boundary (0 < x < a(t)) uponwhich Dirichlet or mixed boundary conditions are specified. Here a(t) is assumed to move slower than light and periodically. Moreover, a is continuous, piecewise linear with two independent parameters. Our major concern will be an observation problem which is based measuring, at each t > 0, of the transverse velocity at a(t). The key to the results is the use of a reduction theorem by Yoccoz [14].

On iterative roots of homeomorphisms of the circle

Zdun M.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 2

203-213

In this paper we deal with the problem of existence and uniqueness of continuous iterative roots of homeomorphisms of the circle. Let F : [S^1 --> S^1] be a homeomorphism without periodic points. If the limit set of the orbit [F^k(z), k belongs to Z] equals [S^1], then F has exactly n iterative roots of n-th order. Otherwise F either has no iterative roots of n-th order or F has infinitely many iterative roots depending on an arbitrary function. In this case we determined all iterative roots of n-th order of F.