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

Nalini Joshi·Johannes A. Petersen
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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 Painlevé test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.

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BibTeXRIS

Nalini Joshi, Johannes A. Petersen. 1996-10-31. Complex Blow-Up in Burgers' Equation: an Iterative Approach. https://arxiv.org/abs/solv-int/9610013

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