Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory (Q388465)

The authors consider a nonlinear Timoshenko system in the whole line. The system is weakly damped by a viscoelastic term in one of the components. This extremely weak dissipation does not allow the use of the well-known time-weighted energy method. To remedy to this, the authors assumed a stronger nonlinearity assumption than the usual one. Under further reasonable smallness and regularity assumptions, global existence and optimal decay results are proved.