# American Institute of Mathematical Sciences

December  2007, 2(4): 733-750. doi: 10.3934/nhm.2007.2.733

## Adjoint calculus for optimization of gas networks

 1 Technische Universität Kaiserslautern, Fachbereich Mathematik, Postfach 3049, D-67653 Kaiserslautern, Germany, Germany

Received  March 2007 Revised  August 2007 Published  September 2007

We consider an optimization problem arising in the context of gas transport in pipe networks. To compensate the pressure loss due to friction and to guarantee a desired (time dependent) outflow profile, compressor stations are included in the network. These compressor stations are relatively cost-intensive, so that a cost effective control is required. In the presented model the compressors are special vertices of the network. We derive an adjoint calculus for gas networks to solve the optimization problem and prove well–posedness of forward and adjoint coupling conditions. Furthermore, numerical examples illustrate the obtained results.
Citation: Michael Herty, Veronika Sachers. Adjoint calculus for optimization of gas networks. Networks & Heterogeneous Media, 2007, 2 (4) : 733-750. doi: 10.3934/nhm.2007.2.733
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