Multidimensional viscoelasticity equations with nonlinear damping and source terms Original Research Article

In this paper we study the initial boundary value problem of multidimensional viscoelasticity equations where View the MathML source is a bounded domain, (σi(s1)−σi(s2))(s1−s2)>0, f(s)s⩾0, g(s)s⩾0 and satisfy some growth conditions. First we introduce a family of potential wells by using a new method. Then using it we obtain some new existence theorems of global solutions and behaviour of vacuum isolation of solutions