Linear Semigroups

  • George R. Sell
  • Yuncheng You
Part of the Applied Mathematical Sciences book series (AMS, volume 143)


In this chapter we describe the basic notions of a linear C 0-semigroup and the related concepts of an infinitesimal generator. These concepts form infinite dimensional versions of solutions of the finite dimensional linear ordinary differential equation ə t x = Ax.In particular, the C 0-semigroup corresponds to the solution operator or the fundamental solution matrix, and the infinitesimal generator corresponds to the linear coefficient matrix A. We will see that the C 0-semigroups are linear prototypes of the semiflows described in Chapter 2.


Hilbert Space Banach Space Dirichlet Boundary Condition Mild Solution Fractional Power 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • George R. Sell
    • 1
  • Yuncheng You
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA

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