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A differentiation index for partial differential-algebraic equations. (English) Zbl 0956.35026
Summary: A differentiation index for nonlinear partial differential-algebraic equations is presented. Determination of the differentiation index with respect to a direction in the space of independent variables uncovers all equations that must be satisfied by the Cauchy data on the hyperplane orthogonal to that direction. This index is thus a generalization of the differentiation index of differential-algebraic equations. The motivation for this work is consistent initialization of partial differential-algebraic systems. The analysis is demonstrated through several examples, including some taken from fluid dynamics and chemical engineering.
MSC:
35G25Initial value problems for nonlinear higher-order PDE
34A09Implicit equations, differential-algebraic equations