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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Special points on first order partial differential equations and the deformations of solutions
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by Marek Kossowski PDF
Trans. Amer. Math. Soc. 302 (1987), 171-184 Request permission

Abstract:

The object of this paper is to identify four cases of special behavior in a class of first order PDE for a real valued function. (The class of PDE may be thought of as perturbation of PDE with singular solutions.) In each case we show how invariants of the PDE determine properties of solutions. The properties of solutions examined here are the structure of critical points and singularities induced by cotangent projection. These properties are described in the sense of constructing local models for solutions and characterizing their behavior under small deformations. We will find two cases where deformations exhibit bifurcation phenomena, and describe generic deformations.
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 171-184
  • MSC: Primary 35A30; Secondary 35B32, 35F20, 58A20, 58C27, 58F14
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0887504-0
  • MathSciNet review: 887504