Dichotomy of Linear Partial Differential Equations of Neutral Type in Banach Spaces

This present paper is mainly devoted to investigate the property of spectral decomposition of neutral differential equations in infinite dimensional setting, that is the exponential dichotomy. In fact, we prove that the exponential dichotomy of the associated semigroup to such equations does not depend on that of their associated difference equations. Based on the regular linear systems and feedback theory, we introduce a new transformation of neutral-type equations which plays a key role in our investigation.