Global existence and blow-up phenomena for a nonlinear wave equation

Global nonexistence of positive initial energy solution for coupled quasilinear system

“…For the case of ρ =0 and ρ i ≠1, Hao et al . studied existence and blowup for a single wave equation with negative initial energy. Wu et al .…”

“…Few results can be found for the case ρ ≠0 and ρ i ( s )≢1 with the positive initial energy although many results have been obtained for the case ρ ≠0 and ρ i ( s )≡1. Mainly inspired by paper , we study the global nonexistence of the system under the assumptions (A1)–(A4). We use the perturbed energy method to show that the solution of with positive initial energy blows up when .…”

Global existence and blowup of solutions for nonlinear coupled wave equations with viscoelastic terms

“…Then it has been improved by Levine and Todorova that the solution blows up with positive initial energy. For other related results of single wave equation, we refer the reader to the works in .…”

Global Existence and Blow-Up for the Euler-Bernoulli Plate Equation with Variable Coefficients

“…The blow-up result is extended by Levine and Serrin [5] to the case of negative initial energy and > 1 (and to abstract evolution problems). Hao et al [6] studied the nonlinear wave equations with damping and source term. By using the energy compensation method, the authors proved the growth orders of the nonlinear strain term, the damping term, and the source term.…”