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On the existence of optimal controls for quasilinear parabolic partial differential equations

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Abstract

A class of systems governed by quasilinear parabolic partial differential equations with first boundary conditions is considered. Existence of solutions for this class of systems and theira priori estimates are established. Further, a theorem on the existence of optimal controls for the corresponding control problem is obtained. Its proof is based on Filippov's implicit functions lemma. The control restraint setU is taken as a measurable multifunction.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of New South Wales, Kensington, Australia

    E. S. Noussair (Senior Lecturer)

  2. Department of Mathematics, Bandung Institute of Technology, Bandung, Indonesia

    S. Nababan (Lecturer)

  3. Department of Applied Mathematics, University of New South Wales, Kensington, Australia

    K. L. Teo (Senior Lecturer)

Authors
  1. E. S. Noussair
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  2. S. Nababan
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  3. K. L. Teo
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Additional information

Communicated by L. Cesari

The authors wish to thank Professor L. Cesari for his most valuable comments and suggestions. In fact, a condition assumed in the original version of this paper was substantially relaxed by him. For details, see Remark 4.1.

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Noussair, E.S., Nababan, S. & Teo, K.L. On the existence of optimal controls for quasilinear parabolic partial differential equations. J Optim Theory Appl 34, 99–115 (1981). https://doi.org/10.1007/BF00933359

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