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Volume 20, Issue 1
Global Nonexistence of the Solutions for a Nonlinear Wave Equation with Q-Laplacian Operator

Hongjun Gao & Hui Zhang

J. Part. Diff. Eq., 20 (2007), pp. 71-79.

Published online: 2007-02

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  • Abstract

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.

  • Keywords

q-Laplacian operator nonlinear wave equation global nonexistence

  • AMS Subject Headings

34G20 35L70 35L99.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-20-71, author = {Hongjun Gao and Hui Zhang }, title = {Global Nonexistence of the Solutions for a Nonlinear Wave Equation with Q-Laplacian Operator}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {1}, pages = {71--79}, abstract = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5294.html} }
TY - JOUR T1 - Global Nonexistence of the Solutions for a Nonlinear Wave Equation with Q-Laplacian Operator AU - Hongjun Gao & Hui Zhang 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 -

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.

Hongjun Gao and Hui Zhang . (2007). Global Nonexistence of the Solutions for a Nonlinear Wave Equation with Q-Laplacian Operator. Journal of Partial Differential Equations. 20 (1). 71-79. doi:
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