Existence and Exponential Decay for a Kirchhoff]Carrier Model with Viscosity

In this work we study the existence of global solutions and exponential decay for the following nonlinear problem: ­ 2 y ­ yM H<=y<2dx D yy D ysf in QsV= 0, `., 2 / ­ t V ­ t ys0 onS1sG1= 0, `., ­ y ­ ­y ). M H<=y<2dx q sg on S sG = 0, `., 0 0 / / V ­n ­ t ­n ­ y y 0. sy0, 0. sy1 in V, ­ t where M is a C1 function, M l.Gl0)0; ;l G0.