A uniqueness theorem is proved
for weak solutions of quasilinear second-order hyperbolic equations of the
form
in many space variables. The weak solutions are assumed to satisfy a time-wise
upper Lipschitz bound
for all 0 < t ≦ t1,t2 where K(t) is an L1-function. Together with the obvious
assumptions, the equation is supposed to satisfy a symmetry condition
along with convexity of the ai in u and uk. As a corollary, a uniqueness theorem for
systems proved by Oleinik is generalized.
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