期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1982
卷号：79
期号：12
页码：3933-3934
DOI：10.1073/pnas.79.12.3933
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：The paper deals with strict solutions u(x,t) = u(x1,x2,x3,t) of an equation [Formula: see text] where Du is the set of four first derivatives of u. For given initial values u(x,0)={varepsilon}F(x), ut(x,0)={varepsilon}G(x), the life span T({varepsilon}) is defined as the supremum of all t to which the local solution can be extended for all x. Blowup in finite time corresponds to T({varepsilon}) < {infty}. Examples show that this can occur for arbitrarily small {varepsilon}. On the other hand, T({varepsilon}) must at least be very large for small {varepsilon}. By assuming that aik,F,G [unk] C{infty
