ALMOST PERIODIC SOLUTIONS FOR A WEAKLY DISSIPATED HYBRID SYSTEM

作者：Micu Sorin^*; Pazoto Ademir F

来源：Mathematical Control and Related Fields, 2014, 4(1): 101-113.

DOI：10.3934/mcrf.2014.4.101

• Almost periodic solutions
• non-homogeneous hyperbolic system
• hybrid system
• Fourier expansion
• Ingham's inequality

We consider a hybrid system coupling an elastic string with a rigid body at one end and we study the existence of an almost periodic solution when an almost periodic force f acts on the body. The weak dissipation of the system does not allow to show the relative compactness of the trajectories which generally implies the existence of such solutions. Instead, we use Fourier analysis to show that the existence or not of the almost periodic solutions depends on the regularity and the exponents of the almost periodic nonhomogeneous term f.

• 出版日期2014-3