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Complex blow-up in Burgers' equation: an iterative approach

Published online by Cambridge University Press:  17 April 2009

Nalini Joshi  and
Johannes A. Petersen
Nalini Joshi
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia, e-mail: [email protected]
Johannes A. Petersen
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia, e-mail: [email protected]
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Abstract

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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

References

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