International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 23, Pages 1433-1445
doi:10.1155/S0161171203209157

Linear neutral partial differential equations: a semigroup approach

Rainer Nagel and Nguyen Thieu Huy

 Arbeitsgemeinschaft Funktionalanalysis (AGFA) Mathematisches Institut der Universität Tübingen, Auf der morgenstelle 10, Tübingen 72076, Germany
Received 17 September 2002

Abstract

We study linear neutral PDEs of the form (∂/∂t)Fut=BFut+Φut, t≥0; u0(t)=φ(t), t≤0, where the function u(⋅) takes values in a Banach space X. Under appropriate conditions on the difference operator F and the delay operator Φ, we construct a C0-semigroup on C0(ℝ−,X) yielding the solutions of the equation.