Pointwise Stabilization for Coupled Quasilinear and Linear Wave Equations

摘要

A large structure is formed by the coupling of simple structural elements. This paper considers the simplest type of such structures which is made up of two coupled strings modelled by quasilinear or linear wave equations. Two stabilizers are installed: one at the left boundary and one at an in-span point. The exponential stability property of this coupled dynamic structure is studied. The method of characteristics, and a frequency domain theorem due to F.L. Huang are used. For the quasilinear case, one can determine various parameters so that the system is exponentially stable for sufficiently small data. For the linear case, installing a stabilizer at a boundary point is robust for the exponential stability of the system.