Study of a model for the equations of inserted elastic string in a thermal environment Original Research Article

In this paper we prove the uniqueness and existence of global solutions for a coupled thermal-Kirchhoff system with Newmann boundary conditions and we show that the solution decomposes into two parts, one of them decays exponentially to zero as time goes to infinity; that is, by denoting E(t)E(t) as the first-order energy of the system, we show that the positive constants CC and γγ exist which satisfy E(t)⩽CE(0)e-γt.E(t)⩽CE(0)e-γt. Turn MathJax on