Completion to involution and semidiscretisations
The paper presents the formal concept of involution indices for differential algebraic equations. Starting with over-determined systems of partial differential equations with linear coefficients and no or periodic boundary conditions differential algebraic systems are obtained using semidiscretization. It is shown that the original partial differential equation is involutive if and only if the semi-discretized equations do not contain hidden constraints. Existence and uniqueness results for smooth solutions are proven by lifting a classical result for hyperbolic systems in Cauchy-Kovalevskaya form to overdetermined systems. Using finite difference and spectral methods for semi-discretization an equivalence between the integrability of the differential algebraic system and the property of the original system to be involutive is shown.
scientific article; zbMATH DE number 1787747