Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional–differential equations and applications

The paper considers the existence and uniqueness of pseudo almost periodic (mild) solutions to some classes of first-order partial neutral functional–differential equations. Upon making some suitable assumptions, existence and uniqueness results are obtained. Applications include both a partial integro-differential equation arising in control systems and the scalar reaction–diffusion equation with delay. © 2006 Elsevier Inc. All rights reserved