GLOBAL EXISTENCE RESULTS FOR LINEAR ANALYTIC PARTIAL-DIFFERENTIAL EQUATIONS

By means of a continuity method some global existence theorems are pro ved, relating the existence domains of the solutions of non-characteri stic Cauchy problems to the growth of the leading coefficients of the equation. This is done in C(n+1) and R(n+1) as corollaries existence r esults due to Persson and Miyake are obtained. Also, some results by d al Fabbro, Furioli Martinolli, and Ricci, as well as by Jannelli and K ajitani, are extended. Corresponding theorems are proved for real anal ytic hyperbolic equations. (C) 1995 Academic Press, Inc.