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Controllability for parabolic equations with uniformly bounded nonlinear terms

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Abstract

We consider a control system for a parabolic equation in a Banach space with uniformly bounded nonlinear termF,

$$dz(t)/dt + Az(t) = F(t, z(t)) + Bf(t), t > 0.$$

Here,Bf(t) corresponds to a finite-dimensional control. We prove the equivalence of approximate controllability for the above nonlinear system and that for the linear system

$$dz(t)/dt + Az(t) = Bf(t), t > 0.$$

Our method is based on results on approximate controllability for linear parabolic systems and estimates of solutions. A practical example is also given for a diffusion and reaction model.

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Authors and Affiliations

  1. Department of Mathematics, College of Arts and Sciences, University of Tokyo, Komaba, Meguro, Tokyo, Japan

    M. Yamamoto (Associate Professor)

  2. Department of Mathematics, Pusan National University, Pusan, Korea

    J. Y. Park (Professor)

Authors
  1. M. Yamamoto
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  2. J. Y. Park
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Communicated by R. Conti

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Yamamoto, M., Park, J.Y. Controllability for parabolic equations with uniformly bounded nonlinear terms. J Optim Theory Appl 66, 515–532 (1990). https://doi.org/10.1007/BF00940936

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