Annali di Matematica Pura ed Applicata

, Volume 124, Issue 1, pp 13–38 | Cite as

Existence of optimal controls for systems governed by parabolic partial differential equations with Cauchy boundary conditions

  • D. W. Reid
  • K. L. Teo


This paper considers the existence of optimal controls for systems governed by a second order parabolic partial differential equation in divergence form with Cauchy conditions. As preliminary results, theorems concerning the convergence of the sequence of weak solutions corresponding to a sequence of admissible controls are proved. Two general forms of criteria are considered. The first one is taken as a function of the weak solution of the system, and the other is taken as a function of the solution of the system and control. Several theorems and corollaries on the existence of optimal controls are then presented.


Boundary Condition Differential Equation Partial Differential Equation Weak Solution Divergence Form 
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Copyright information

© Nicola Zanichelli Editore 1980

Authors and Affiliations

  • D. W. Reid
    • 1
  • K. L. Teo
    • 1
  1. 1.SydneyAustralia

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