A General Hyperbolic Model for Networks of One Dimensional Elements

Abstract

In this chapter we study a general linear, hyperbolic model for vibrating networks of one-dimensional elements. This model accommodates not only the elastic string networks of Chapter II, but also applies to networks of beams governed by one or other of the linear, isothermal, hyperbolic beam models of Chapter III and to mixed networks which contain both beams and strings. The existence and regularity of solutions to the general network system is established, along lines identical to those used in Section 4 of Chapter II. Energy estimates involving characteristics are proved and then used to obtain the estimates from which exact controllability and stabilizability follow for networks containing no closed loops, again following the argument used in Chapter II.