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Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 258))

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There is a well-known theorem, called the Cauchy—Kowaleski theorem, which asserts that there exists a unique analytic solution of an analytic initial-value problem. Here, by an analytic initial-value problem, we mean a problem in which everything (the terms in the equation, the initial data, and the initial hypersurface), is analytic in a neighbourhood of a point (see [Ga]). The possibility is thereby left open as to whether there can exist a nonanalytic solution to this problem. Holmgren’s uniqueness theorem denies this possibility. We shall also find this result useful in Chapter 6 where we shall apply it to determine qualitative information on domains of dependence. For this reason, we shall prove a rather general version of the theorem.

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© 1983 Springer-Verlag New York Inc.

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Smoller, J. (1983). Holmgren’s Uniqueness Theorem. In: Shock Waves and Reaction—Diffusion Equations. Grundlehren der mathematischen Wissenschaften, vol 258. Springer, New York, NY.

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-0154-7

  • Online ISBN: 978-1-4684-0152-3

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