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Conditions for periodic vibrations in a symmetric n-string

100%
Gauthier C.
Open Mathematics
|
2008
|
tom 6
|
nr 2
287-300
EN
A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.
2
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Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients

81%
Li H., Ji S.
Open Mathematics
|
2011
|
tom 9
|
nr 2
269-280
EN
This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation. Furthermore, the existence of the optimal control is proved by means of the Arzelà-Ascoli lemma and Sobolev compact imbedding theorem.
3
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Blow-up of solutions for a viscoelastic equation with nonlinear damping

81%
Zhifeng Y.
Open Mathematics
|
2008
|
tom 6
|
nr 4
568-575
EN
The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.
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