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Complex blow-up in Burgers' equation: an iterative approach
Published online by Cambridge University Press: 17 April 2009
Abstract
We show that for a given holomorphic noncharacteristic surface S ∈ ℂ2, and a given holomorphic function on S1 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 Painlevé test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 353 - 362
- Copyright
- Copyright © Australian Mathematical Society 1996
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