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.
KeywordsHilbert Space Banach Space Dirichlet Boundary Condition Mild Solution Fractional Power
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