TY - JOUR
T1 - Global Nonexistence of the Solutions for a Nonlinear Wave Equation with Q-Laplacian Operator
JO - Journal of Partial Differential Equations
VL - 1
SP - 71
EP - 79
PY - 2007
DA - 2007/02
SN - 20
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5294.html
KW - q-Laplacian operator
KW - nonlinear wave equation
KW - global nonexistence
AB - <p>We study the global nonexistence of the solutions of the nonlinear q-Laplacian wave equation u_{tt}-Δ_qu+(-Δ)^αu_t=|u|^{p-2}u, 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.</p>