TY - JOUR
T1 - A Critical Value for Global Nonexistence of Solution of a Wave Equation
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 - <p>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 &gt; p(2) there may exist a global solution and when 1 &lt; p &lt; 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) &lt; p &lt; 5.</p>