= Uniform Cauchy radius for polynomial forcing
For a linear <real analytic> non-characteristic <Cauchy problem for a partial differential equation> with zero data, the local <real analytic> radius may be chosen uniformly over <polynomial> forcing terms. Fix an analyticity exponent $R^{-1}$. Each <polynomial>, including a <polynomial> obtained by a <polynomial> coordinate change, satisfies the corresponding factorial <derivative> bound with some finite prefactor, uniformly over a compact parameter range. Divide the forcing by that prefactor to put all such data in one fixed majorant class. The <Cauchy-Kovalevskaya theorem> supplies a common radius, and linearity rescales the solution back without shrinking it. This argument does not bound the amplitudes of the resulting solutions uniformly.
Back to article page
