Abstract:
In this paper estimates are obtained for the solution of the Cauchy problem with data on a timelike surface in the case of the nonelliptic analytic system of second order
$$
A_{ij}u_{x_ix_j}+B_iu_{x_i}+Cu=0
$$
($i,j=0,1,\dots,n$; $A_{ij},B_i,C$ are $N\times N$ matrices) in which the operator $\sum_{i,j=0}^nA_{ij}\partial^2/\partial x_i\partial x_j$ is elliptic and the dependence of the estimate on the dimension of the support is given explicitly. On the basis of these estimates the author solves the problem of the rate of decay of the solution and its first derivatives in the neighborhood of a zero on the boundary of the domain of the solution that suffices for the solution to vanish in some region.
Bibliography: 7 titles.
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