Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay

Danhua Wang, Gang Li, Biqing Zhu
2016 Journal of Nonlinear Science and its Applications  
In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and a delay term. Under appropriate hypotheses on the relaxation function and the relationship between the weight of the damping and the weight of the delay, we prove the well-posedness result by using Faedo-Galerkin method. By introducing suitable Lyapunov functionals, we establish a general decay result, from which the exponential and polynomial types of decay are only special cases.
doi:10.22436/jnsa.009.03.46 fatcat:cou4x4mb45h6viwlavm35oxtg4