Existence for large times of finite amplitude elastic waves arising from small disturbances.
This paper deals with strict solutions u(i)(t, x(1), x(2), x(3)) of a system of quasi-linear equations [Formula: see text] with u' = ([unk](x(i) )u(k)), and i, k, r, s ranging over 1, 2, 3. For given initial conditions u(i) = epsilonf(i)(x(1), x(2), x(3)), [unk](t)u(i) = epsilong(x(1), x(2), x(3)) for t = 0 the life-span T(epsilon) is the supremum of all t > 0 to which the u(i) can be extended as strict solutions for all x. It is shown that lim inf(epsilon-->0) epsilon log T(epsilon) > 0 for C(ikrs), f(i), g(i) [unk] C(0) (infinity), and C(ikrs) = C(rsik), C(ikrs)(0) = 0.
John
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Courant Institute of Mathematical Sciences, New York University, New York, NY 10012.