TITLE: Estimate for radius of convergence of solutions given by Cauchy-Kovalevskaya Theorem
QUESTION [7 upvotes]: I'm sure you can extract it from the proof, but does anyone know of a reference where the radius of convergence (in terms of radius of convergence of the initial data and PDE) of the solution given by the Cauchy-Kovalevskaya Theorem is written down?
On a related, but more speculative note, I'm curious if there are any results along the following lines:  Suppose one is given a problem solvable by the Cauchy-Kovalevskaya Theorem along with a real analytic solution with uniform lower bound on its radius of convergence (alternatively which exists in some uniform strip about the hypersurface on which initial data is prescribed).  If one approximates the data of the given solution (the right notion is part of the question) by some sequence of real analytic data, can one say anything about the radius of convergence of the corresponding solutions (or size of strip the solutions exist on).

REPLY [3 votes]: Theorem 9.4.5 in the first volume of Hörmander's four-volume treatise "The Analysis of Linear Partial Differential Operators" is a quantitative version of the Cauchy-Kovalevsky theorem. Condition (9.4.7) of that theorem gives bounds on the radii of convergence. The theorem is stated with zero initial data. To apply it with non-zero initial data, first move these into the right-hand side of the equation by applying the differential operator to the Taylor polynomial (in $z_n$) of the initial data.