The Blow-Up of Solutions for a Class of Semi-linear Equations with p-Laplacian Viscoelastic Term Under Positive Initial Energy

This paper deals with homogeneous Dirichlet boundary value problem to a class of semi-linear equations with p-Laplacian viscoelastic term?u/?t - ?u + ?(t)(0)g(t - s)?(p)u(x, s)ds = |u|(q(x)-2) u, x ? O, t = 0, 0 the bounded domain O C R-n (n = 3) with a smooth boundary. We prove that the weak solutions of the above problems blow up in finite time for all 2k < q(-) < q(+) < p < 2n/n-2 (k is defined in (2.5)), when the initial energy is positive and the function g satisfies suitable conditions. This result generalized and improved the result by Messaoudi (Abstr Appl Anal 2005(2):87-94, 2005).