(untitled) (Journal of Partial Differential Equations, 2007)
We study the global nonexistence of the solutions of the nonlinear q-Laplacian wave equation u_tt-Δ_qu+(-Δ)^αu_t=|u|^p-2u, where 0 ‹ α ≤ 1, 2 ≤ q ‹ p. We obtain that the solution blows up in finite time if the initial energy is negative. Meanwhile, we also get the solution blows up in finite time with suitable positive initial energy under some conditions.