The Cauchy-Kovalevskaja Theorem

Marcelo R. Ebert and Michael Reissig
Additional contact information
Marcelo R. Ebert: University of São Paulo, Department of Computing and Mathematics
Michael Reissig: TU Bergakademie Freiberg, Institute of Applied Analysis

Chapter Chapter 4 in Methods for Partial Differential Equations, 2018, pp 37-48 from Springer

Abstract: 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.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-66456-9_4

Ordering information: This item can be ordered from
http://www.springer.com/9783319664569

DOI: 10.1007/978-3-319-66456-9_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().