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Linear Semigroups

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

Abstract

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.

Keywords

Hilbert Space Banach Space Dirichlet Boundary Condition Mild Solution Fractional Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Additional Readings

  1. R S Phillips, See Hille and Phillips.Google Scholar
  2. N Dunford and J T Schwartz (1958), Linear Operators, Parts 1, 2 and 3, Wiley Inter-science, New York.Google Scholar
  3. K-J Engel and R Nagel (2000), One-Parameter Semigroups for Linear Evolution Equations, Springer Verlag, New York.MATHGoogle Scholar
  4. A Friedman (1969), Partial Differential Equations, Holt Rinehart and Winston, New York.MATHGoogle Scholar
  5. J A Goldstein (1985), Semigroups of Linear Operators and Applications, Oxford Univ Press, Oxford.MATHGoogle Scholar
  6. D B Henry (1981), Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, No 840, Springer Verlag, New York.Google Scholar
  7. T Kato (1961), Fractional powers of dissipative operators, J Math Soc Japan 13, 246–274.Google Scholar
  8. S G Krein (1971), Linear Differential Equations in Banach Spaces, Translations of Math Monographs, Vol 29, Am Math Soc, Providence.Google Scholar
  9. A Pazy (1983), Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Vol 44, Springer Verlag, New York.Google Scholar
  10. H Triebel (1978), Interpolation Theory, Function Spaces and Differential Operators, VEB Deutscher Verlag der Wissenschaften, Berlin.Google Scholar
  11. K Yosida (1980), Functional Analysis, Springer Verlag, New York.MATHCrossRefGoogle Scholar

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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