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Complex Blow-Up in Burgers' Equation: an Iterative Approach

Authors
  • Joshi, Nalini
  • Petersen, Johannes A.
Type
Preprint
Publication Date
Oct 30, 1996
Submission Date
Oct 30, 1996
Identifiers
arXiv ID: solv-int/9610013
Source
arXiv
License
Unknown
External links

Abstract

We show that for a given holomorphic noncharacteristic surface S in two-dimensional complex space, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlev\'e test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.

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