Asymptotic behavior of a logarithmic-viscoelastic wave equation with internal fractional damping
摘要
We consider a viscoelastic wave equation with internal fractional damping and a logarithmic source term. By utilizing the energy method combined with the Faedo–Galerkin procedure, we establish the existence of a global solution. Furthermore, we demonstrate that, under the general assumption on the relaxation function g, the global solutions exhibit a general decay behavior. This is achieved by constructing a suitable Lyapunov functional.