A Critical Value for Global Nonexistence of Solution of a Wave Equation

A Critical Value for Global Nonexistence of Solution of a Wave Equation

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