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
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.