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We consider a non-overlapping domain decomposition method for an optimal control problem related to the flow of gas in a pipe network. The equations of motions are taken to be represented by a friction dominated model derived from a semi-linear approximation of the fully nonlinear isothermal Euler gas equations. This involves a p-Laplace-type problem on the graph with \(p=\frac{3}{2}\) . We continue the work [15] where such a problem has been discussed in the context of an instantaneous control strategy. We provide a non-overlapping domain decomposition in the spirit of P.L. Lions for the corresponding quasilinear elliptic problems and extend the method to the first order optimality system.

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Nonoverlapping Domain Decomposition for Instantaneous Optimal Control of Friction Dominated Flow in a Gas-Network

  • 会议论文

  • 发表日期：

    2025年

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  • Günter Leugering

摘要

We consider a non-overlapping domain decomposition method for an optimal control problem related to the flow of gas in a pipe network. The equations of motions are taken to be represented by a friction dominated model derived from a semi-linear approximation of the fully nonlinear isothermal Euler gas equations. This involves a p-Laplace-type problem on the graph with \(p=\frac{3}{2}\) . We continue the work [15] where such a problem has been discussed in the context of an instantaneous control strategy. We provide a non-overlapping domain decomposition in the spirit of P.L. Lions for the corresponding quasilinear elliptic problems and extend the method to the first order optimality system.