Existence and general decay for the full von Karman beam with a thermo-viscoelastic damping, frictional dampings and a delay term

摘要

In this paper, we study the global existence and general decay rate for a one-dimensional full von Karman beam with a thermo-viscoelastic damping, frictional dampings and a delay term in the internal feedback. First, we use the Faedo-Galerkin approximations together with energy estimates to obtain the existence and uniqueness of the global solutions. Then, by introducing suitable energy and Lyapunov functionals, under a hypothesis between the weight of the delay term and the weight of the friction damping term in the internal feedback, we establish a general decay rate result for the energy, which allows a wider class of relaxation functions, and thus generalize some previous results existing in the literature.