Multidimensional viscoelasticity equations with nonlinear damping and source terms

In this paper we study the initial boundary value problem of multidimensional viscoelasticity equations u(n) - Deltau(t) - Sigma(i=1)(N) partial derivative/partial derivativex(i) sigma(i)(u(xi)) + f(ut) = g(u), x is an element of Omega, t > 0, u(x, 0) = u(0)(x), u(t)(x, 0) = u(1)(x) x is an element of Omega, u(x,t) = 0, x is an element of partial derivativeOmega, t greater than or equal to 0, where Omega subset of R-N is a bounded domain, (sigma(i)(s(1)) - sigma(i)(s(2)))(s(1) - s(2)) > 0, f(s)s greater than or equal to 0, g(s)s greater than or equal to 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. (C) 2003 Elsevier Ltd. All rights reserved.