Spencer δ-cohomology, restrictions, characteristics and involutive symbolic PDEs
نویسندگان
چکیده
We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results relating involutivity, restrictions, characteristics and characteristicity, known for first order systems, extend to the general context. This involves, in particular, a new definition of strong characteristicity. The proof exploits a spectral sequence relating Spencer δ-cohomology of a symbolic system and its restriction to a non-characteristic subspace. 1
منابع مشابه
Mayer Brackets and Solvability of Pdes – Ii
For the Spencer δ-cohomologies of a symbolic system we construct a spectral sequence associated with a subspace. We calculate the sequence for the systems of Cohen-Macaulay type and obtain a reduction theorem, which facilitates computation of δ-cohomologies by reducing dimension of the system. Using this algebraic result we prove an efficient compatibility criterion for a system of two scalar n...
متن کاملCompatibility, multi-brackets and integrability of systems of PDEs
We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators. These multi-brackets generalize the higher JacobiMayer brackets, important in the study of evolutionary equations and the integrability problem. We also calculate Spencer δ-cohomology of generalized complete intersections and eval...
متن کاملSimplifying Numerical Solution of Constrained Pde Systems through Involutive Completion
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 genera...
متن کاملHopf–cyclic Homology and Relative Cyclic Homology of Hopf–galois Extensions
The determination of cyclic (co)homology of a given algebra is a quite important and difficult problem. Let us briefly recall some of the results obtained that are somehow related to our paper. The cyclic homology of group algebras over fields of characteristic 0 was computed by Burghelea, [3]. For a complete algebraic proof of Burghelea’s result the reader is referred to [19], while a relative...
متن کاملReduction of Systems of Nonlinear Partial Diierential Equations to Simpliied Involutive Forms
We describe the rif algorithm which uses a nite number of diierentiations and algebraic operations to simplify analytic nonlinear systems of partial diierential equations to what we call reduced involutive form. This form includes the integrability conditions of the system and satisses a constant rank condition. The algorithm is useful for classifying initial value problems for determined pde s...
متن کامل