Complex Blow-Up in Burgers' Equation: an Iterative Approach
solv-int
2008-02-03 v1 Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.solv-int/9610013,
title = {Complex Blow-Up in Burgers' Equation: an Iterative Approach},
author = {Nalini Joshi and Johannes A. Petersen},
journal= {arXiv preprint arXiv:solv-int/9610013},
year = {2008}
}
Comments
11 pages in LaTeX. To appear in Bull. Aust. Math. Soc