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Volume 5, Issue 3
Blow Up of Classical Solutions to $\Box$ U=|u|1+α in Three Space Dimensions

Zhou Yi

J. Part. Diff. Eq., 5 (1992), pp. 21-32.

Published online: 1992-05

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  • 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}.
  • Keywords

Classical solution life span blow up

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@Article{JPDE-5-21, author = {}, title = {Blow Up of Classical Solutions to $\Box$ U=|u|1+α in Three Space Dimensions}, journal = {Journal of Partial Differential Equations}, year = {1992}, volume = {5}, number = {3}, pages = {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}.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5742.html} }
TY - JOUR T1 - Blow Up of Classical Solutions to $\Box$ U=|u|1+α 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}.
Zhou Yi. (1970). Blow Up of Classical Solutions to $\Box$ U=|u|1+α in Three Space Dimensions. Journal of Partial Differential Equations. 5 (3). 21-32. doi:
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