Alphabeta MathHow statement and proof provenance work
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The analytic existence and uniqueness boundary
Remarks
Cauchy–Kovalevskaya on a noncharacteristic analytic hypersurface gives existence and uniqueness of analytic germs under its specified total-order and normal-order conditions. It does not assert an analytic solution for smooth nonanalytic initial data, or continuous dependence in any smooth topology. In particular an equation solved for a time derivative is not automatically in the required normal form: a right-hand derivative of higher total order violates that formulation. The proof above uses no recorded-not-proved CK result.
Source notes
Gantumur, §4 Example 21 and §5 characteristic discussion, printed pp. 11–14; the analytic-germ theorem above fixes the local scope.
Depends on
Used by
- Analytic heat data need not give a time-analytic germ Counterexample
Dependency tree · two levels
6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Gantumur, Math 580 Lecture Notes 2: The Cauchy-Kovalevskaya Theorem (standard reference, not scraped)
- Ageno, Part III: Analysis of Partial Differential Equations (standard reference, not scraped)