Involutive Hyperbolic Differential Systems
Deane Yang
jan. 1987 · American Mathematical Society: Memoirs of the American Mathematical Society 370. knjiga · American Mathematical Soc.
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The Cartan-Kähler theorem demonstrates that certain real analytic exterior differential systems--ones which Cartan dubbed "involutive"--admit local real analytic solutions. The proof reduces the system to a set of determined systems of PDE's which are then solved using the Cauchy-Kovalevski theorem. The subtlety in the theorem and in the definition of involutivity lies in checking that the "solution" obtained from the determined systems does in fact satisfy the original differential system.
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