Asymptotic behavior of a planar flexible network with thermal effects

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. Then we obtain that the solution of the network system decays to zero exponentially by the frequency domain method together with the multiplier techniques.