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Optimal control for the dam problem

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Abstract

Consider the variational inequality for the rectangular dam problem and assume that fluid can be withdrawn from the bottom at a rate proportional tok(x). Denote byp(x, y) the pressure of the fluid in the dam corresponding to a particular choice ofk. Consideringk(x) as a control variable varying in a class {0⩽k(x)⩽N, ∫k(x)dx⩽M}, we introduce the functionalJ(k)=∫∫g(y)p(x, y) whereg(y) is a given positive and monotone nondecreasing function. We characterize the controlsk 0 which minimizeJ(k).

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Authors and Affiliations

  1. Department of Mathematics, Northwestern University, 60201, Evanston, IL, USA

    Avner Friedman & Daniel Yaniro

Authors
  1. Avner Friedman
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  2. Daniel Yaniro
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Additional information

Communicated by D. Kinderlehrer

This work is partially supported by National Science Foundation MCS-8300293

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Friedman, A., Yaniro, D. Optimal control for the dam problem. Appl Math Optim 13, 59–78 (1985). https://doi.org/10.1007/BF01442199

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  • DOI: https://doi.org/10.1007/BF01442199

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