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When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several flow equations...
When analysing general systems of PDEs, it is important first to find the involutive form of the initial system.
This is because the properties of the system cannot in general be determined if the system is not involutive.
We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form
of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of
several flow equations...
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
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