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Volume 18, Issue 3
A Critical Value for Global Nonexistence of Solution of a Wave Equation

Zhenchao Cao

J. Part. Diff. Eq., 18 (2005), pp. 263-266.

Published online: 2005-08

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  • Abstract

Consider the Cauchy problem for a wave equation on R²: u_{tt} - Δu = |u|^{p-1}u. In 1981 Glassey gave a guess to a critical value p(2) = \frac{1}{2}(3 + \sqrt{17}): when p > p(2) there may exist a global solution and when 1 < p < p(2) the solution may blow up. By our main result in this paper a counter example to the guess is given that the solution may also blow up in finite time even if p(2) < p < 5.

  • Keywords

Wave equation global nonexistence a guess to critical value

  • AMS Subject Headings

35L05 35L70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-18-263, author = {Zhenchao Cao }, title = {A Critical Value for Global Nonexistence of Solution of a Wave Equation}, journal = {Journal of Partial Differential Equations}, year = {2005}, volume = {18}, number = {3}, pages = {263--266}, abstract = {

Consider the Cauchy problem for a wave equation on R²: u_{tt} - Δu = |u|^{p-1}u. In 1981 Glassey gave a guess to a critical value p(2) = \frac{1}{2}(3 + \sqrt{17}): when p > p(2) there may exist a global solution and when 1 < p < p(2) the solution may blow up. By our main result in this paper a counter example to the guess is given that the solution may also blow up in finite time even if p(2) < p < 5.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5361.html} }
TY - JOUR T1 - A Critical Value for Global Nonexistence of Solution of a Wave Equation AU - Zhenchao Cao JO - Journal of Partial Differential Equations VL - 3 SP - 263 EP - 266 PY - 2005 DA - 2005/08 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5361.html KW - Wave equation KW - global nonexistence KW - a guess to critical value AB -

Consider the Cauchy problem for a wave equation on R²: u_{tt} - Δu = |u|^{p-1}u. In 1981 Glassey gave a guess to a critical value p(2) = \frac{1}{2}(3 + \sqrt{17}): when p > p(2) there may exist a global solution and when 1 < p < p(2) the solution may blow up. By our main result in this paper a counter example to the guess is given that the solution may also blow up in finite time even if p(2) < p < 5.

Zhenchao Cao . (2005). A Critical Value for Global Nonexistence of Solution of a Wave Equation. Journal of Partial Differential Equations. 18 (3). 263-266. doi:
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