Generalized Tableaux and Formally Well-posed Initial Value Problems
نویسنده
چکیده
We generalize the notion of a tableau of a system of partial diierential equations. This leads to an intrinsic deenition of formally well-posed initial value problems, i.e. problems with exactly the right amount of Cauchy data. We must allow here that the data is prescribed on a ag of submanifolds. The advantage of this approach is that even for non-normal systems the data can be chosen completely arbitrarily and does not need to satisfy any constraints. The existence and uniqueness of analytic solutions is guaranteed by the Cartan-KK ahler Theorem. For linear systems the uniqueness is extended to non-analytic solutions by a generalization of the Holmgren Theorem. We discuss the relation between the generalized tableaux and-regularity of the coordinate system and we give a rigorous deenition of under-and over-determinacy.
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