Global existence results for linear analytic partial differential equations (Q1343103)

The author treats the Cauchy problem for complex linear analytic partial differential equations. Some analytic global existence theorems for the Cauchy problem with analytic data are obtained by the sweeping out method introduced by F. John. The main results are general extension theorems where the existence domains of solutions of the Cauchy problem are described in terms of the size of the leading coefficients of the equations, or, equivalently, in terms of the size of the characteristics. Analogous results are obtained in the real case.