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- W2557193726 abstract "In this chapter, we introduce a “model problem”, denoted by ( P P 0 ), of an elliptic boundary value problem, which we will use to describe the use of spatial invariant embedding and the factorized forms that follow from it. The operator for this problem is naturally the Laplacian and a cylindrical domain is assumed. We will that this geometry arises naturally when we make an analogy with the optimal control problem for parabolic systems. However, from the point of view of solving elliptic problems, this geometry is a special case, and the generalization of the spatial invariant embedding method to other shapes of domain will be studied. After defining our model problem and its functional framework, we will show how spatial invariant embedding leads to a system of decoupled evolution equations equivalent to the boundary value problem. Depending on how we choose to determine the family of problems for the invariant embedding, multiple factorizations are possible. We shall present three of them. In this chapter, the computation of derivatives is performed in a formal sense only. Various justifications are possible, we will use a Galerkin method and, we will consider a regularization." @default.
- W2557193726 created "2016-11-30" @default.
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- W2557193726 date "2016-01-01" @default.
- W2557193726 modified "2023-10-16" @default.
- W2557193726 title "Presentation of the Formal Computation of Factorization" @default.
- W2557193726 doi "https://doi.org/10.1016/b978-1-78548-143-7.50001-3" @default.
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