Special points on first order partial differential equations and the deformations of solutions
Author: Marek Kossowski
Journal: Trans. Amer. Math. Soc. 302 (1987), 171-184
MSC: Primary 35A30; Secondary 35B32, 35F20, 58A20, 58C27, 58F14
MathSciNet review: 887504
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.
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