TY - JOUR
T1 - Blow Up of Classical Solutions to $\Box$ U=|u|<sup>1+α</sup> in Three Space Dimensions
JO - Journal of Partial Differential Equations
VL - 3
SP - 21
EP - 32
PY - 1992
DA - 1992/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5742.html
KW - Classical solution
KW - life span
KW - blow up
AB -  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}.