Year: 2005
Journal of Partial Differential Equations, Vol. 18 (2005), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-JPDE-5361
Journal of Partial Differential Equations, Vol. 18 (2005), Iss. 3 : pp. 263–266
Published online: 2005-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 4
Keywords: Wave equation