1994 | OriginalPaper | Buchkapitel
Holmgren’s Uniqueness Theorem
verfasst von : Joel Smoller
Erschienen in: Shock Waves and Reaction—Diffusion Equations
Verlag: Springer New York
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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.