This paper deals with strict solutions ui(t, x1, x2, x3) of a system of quasi-linear equations [Formula: see text] with u′ = ([unk]xiuk), and i, k, r, s ranging over 1, 2, 3. For given initial conditions ui = εfi(x1, x2, x3), [unk]tui = εg(x1, x2, x3) for t = 0 the life-span T(ε) is the supremum of all t > 0 to which the ui can be extended as strict solutions for all x. It is shown that lim infε→0 ε log T(ε) > 0 for Cikrs, fi, gi [unk] C0∞, and Cikrs = Crsik, Cikrs(0) = 0.
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机译：本文研究的是u'=（[unk] xiuk）且i，k，r，s范围为准的拟线性方程组[公式：参见文本]的严格解ui（t，x1，x2，x3）超过1，2，3。对于给定的初始条件ui =εfi（x1，x2，x3），[unk] tui =εg（x1，x2，x 3 ） t = 0，寿命 T （ε）是 u i <的所有 t 可以扩展为所有 x 的严格解决方案。结果表明对于 C ikrs ，f i，lim inf ε→0 εlog T （ε）> 0 ，g i [unk] C 0 ∞和 C ikrs = C rsik ， C ikrs （0） = 0。
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