Blow Up of Classical Solutions to $\Box$ U=|u|<sup>1+α</sup> in Three Space Dimensions

Blow Up of Classical Solutions to $\Box$ U=|u|<sup>1+α</sup> in Three Space Dimensions

Year:    1992

Journal of Partial Differential Equations, Vol. 5 (1992), Iss. 3 : pp. 21–32

Abstract

We study the life span of classical solutions to ◻u = |u|^{1+α} in three space dimensions with initial data t = 0: u = εf(x), u, = εg(x), where f and g have compact support and are not both identically zero, ε is a small parameter. We obtain respectively upper and lower bounds of the same order of magnitude for the life span for sufficiently small ε in case 1 ≤ α ≤ \sqrt{2}. We also proved that the classical solution always blows up even when ε = 1 in the critical case α = \sqrt{2}.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1992-JPDE-5742

Journal of Partial Differential Equations, Vol. 5 (1992), Iss. 3 : pp. 21–32

Published online:    1992-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Classical solution