UNIQUENESS IN A CHARACTERISTIC CAUCHY-PROBLEM WITH VARIABLE MULTIPLICITY

[摘要] For the operator P(c1, c2) = (partial derivative(x) + a1x(k)partial derivative(y) + a2x(k))(partial derivative(x) - b1x(k)partial derivative(y) - b2x(k)) - c1x(k-1)partial derivative(y) - c2x(k-1) with a1.b1>0, a2, b2 is-an-element-of R, c1, c2 is-an-element-of C, we show that the local solutions of the (characteristic) Cauchy problem with data u, u(y) at y = 0, are unique if and only if the pair (c1, c2) does not belong to a discrete set, namely if (c1, c2) not-equal [j(k+1)+l].(a1+b1, a2+b2), for all j is-an-element-of Z, l=0, 1. (C) 1994 Academic Press, Inc.

[发布日期] 1994-02-15