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In this paper, we study the thermal effects on the asymptotic behavior of a simple planar network of elasticities with variable coefficients. Assume that the network consists of three edges. the exterior vertices of the network are clamped. The conservative laws (self-adjoint conditions) are fulfilled at the common vertex. We prove that the network is well-posedness based on the semigroup setting...
In this note, we firstly recall the main results in [1] and their brief proofs. As applications of the results, we study the control problem of the general networks of strings. Some new examples of networks of strings with circuits are given.
In this paper we consider the dynamical stability of a tree-shape networks of Timoshenko beams with time-delay terms in the boundary controls. The time-delay feedback controllers at the exterior vertices are designed to derive the beams back to its equilibrium position. We first get the wellposedness of the closed loop system. Under certain conditions, we show that this system is asymptotically stable...
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