Existence and stability estimate for the solution of the ageing hereditary linear viscoelasticity problem

The paper is concerned with the existence and stability of weak (variational) solutions for the problem of the quasistatic evolution of a viscoelastic material under mixed inhomogenous Dirichlet-Neumann boundary conditions. The main novelty of the paper relies in dealing with continuous-in-time weak solutions and allowing nonconvolution and weak-singular Volterra's relaxation kernels.