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
Arbeitsgemeinschaft Funktionalanalysis (AGFA) Mathematisches Institut
der Universität Tübingen, Auf der morgenstelle 10, Tübingen 72076, Germany
Received 17 September 2002
Copyright © 2003 Rainer Nagel and Nguyen Thieu Huy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.