(untitled) (Journal of Computational Mathematics, 1983)
In this paper we discuss the estimation for solutions of the ill-posed Cauchy problems of the following differential equationdu(t)dt=A(t)u(t)+N(t)u(t),t(0,1), where A(t) is a p. d. o. (pseudo-differential operator(s)) of order 1 or 2, N(t) is a uniformly bounded H-›H linear operator. It is proved that if the symbol of the principal part of A(t) satisfies certain algebraic conditions, two estimates for the solution u(t) hold. One is similar to the estimate for analytic functions in the Three-Circle Theorem of Hadamard. Another is the estimate of the growth rate of ||u(t)|| when A(1)u(1)H.