Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition

Long Nguyen Thanh, Alain Pham Ngoc Dinh, Le Xuan Truong

We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_…