CAUCHY-PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATION OF HIGHER-ORDER WITH DISCONTINUOUS INITIAL DATA

In this paper the following Cauchy problem is under consideration, [GRAPHICS] where L is a strictly hyperbolic operator of m-th order with respect to direction t, F is a C(infinity) function of its arguments, the initial data have discontinuity along a smooth submanifold with codimentional 1 on initial plane and some conormal regularity with respect to manifold.