The applications of C-semigroups to the Dirac equation

摘要

In this paper, we study first-order symmetric, hyperbolic systems of differential operator with constant coefficients on L-P-spaces. We show that such systems can be governed by some C-semigroups and as an application we consider the Dirac equation. Our result improves that of Nicaise [S. Nicaise, The Hille-Yosida and Trotter-Kato theorems for integrated semigroups, J. Math. Anal. Appl. 180 (1993) 303-316]. (C) 2008 Elsevier Ltd. All rights reserved.