Existence for large times of finite amplitude elastic waves arising from small disturbances
AUTOR(ES)
John, Fritz
RESUMO
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.
