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

Hongjun Gao & Hui Zhang

DOI:

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

Published online: 2007-02

Preview Full PDF 290 647
Export citation
  • 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

  • Email address
  • References
  • Hide All
    View All

@Article{JPDE-20-71, author = {}, 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} }
Copy to clipboard
The citation has been copied to your clipboard