Uniqueness and non-uniqueness in the Cauchy problem. (English) Zbl 0574.35002

Alinhac, S.

Microlocal analysis, Proc. Conf., Boulder/Colo. 1983, Contemp. Math. 27, 1-22 (1984).

[For the entire collection see Zbl 0527.00007.]
This paper intends to give a survey of recent results on the question of local uniqueness in the Cauchy problem for operators with \(C^{\infty}\) coefficients, but no proof is given nor the methods described. The content of the paper is the following: 1. Calderon’s theorem; 2. Structural conditions on the operator; 3. Hörmander’s theorem and convexity conditions on the initial surface; 4. Higher order vanishing of the principal symbol and conditions on the lower order terms; 5. The characteristic Cauchy problem.
The paper ends with a quite complete bibliography on the subject.

Reviewer: C.Zuily

MSC:

35A07

Local existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

survey; local uniqueness; Cauchy problem; bibliography