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The Cauchy-Kovalevskaja Theorem

In: Methods for Partial Differential Equations

Author

Listed:
  • Marcelo R. Ebert

    (University of São Paulo, Department of Computing and Mathematics)

  • Michael Reissig

    (TU Bergakademie Freiberg, Institute of Applied Analysis)

Abstract

The classical Cauchy-Kovalevskaja theorem is one of the fundamental results in the theory of partial differential equations. This theorem makes two assertions, on the one hand it yields the local existence of analytic solutions to a large class of Cauchy problems and on the other hand it yields the uniqueness of this solution in the class of analytic functions. This chapter deals not only with the Cauchy-Kovalevskaja theorem in its classical form but in its abstract form in scales of Banach spaces as well. Some applications in the theory of Hele-Shaw flows complete this chapter. These applications serve as an interesting field for verifying the importance of the tool of an abstract form of the Cauchy-Kovalevskaja theorem.

Suggested Citation

  • Marcelo R. Ebert & Michael Reissig, 2018. "The Cauchy-Kovalevskaja Theorem," Springer Books, in: Methods for Partial Differential Equations, chapter 0, pages 37-48, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-66456-9_4
    DOI: 10.1007/978-3-319-66456-9_4
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