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<p>The boundary null controllability for the parabolic Stokes system and the hyperbolic Stokes system is, up to now, obtained via an artificial argument consisting in enlarging the domain, using the results of distributed controllability in a small domain contained in the enlarged part, and then obtaining the boundary controllability by restriction. In the present paper we give in a first part some direct results of boundary controllability for the hyperbolic Stokes system in a star-shaped domain. We then apply the transmutation method to obtain a result of null controllability for the parabolic Stokes system. One interest is that we can characterize the control that we use and this gives a rather surprising result.</p>

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A Direct Approach to the Boundary Controllability of the Hyperbolic Stokes System

  • 期刊论文

  • 发表日期：

    2025年6月12日

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  • F. W. Chaves-Silva,
  • J.-P. Puel,
  • M. C. Santos

摘要

The boundary null controllability for the parabolic Stokes system and the hyperbolic Stokes system is, up to now, obtained via an artificial argument consisting in enlarging the domain, using the results of distributed controllability in a small domain contained in the enlarged part, and then obtaining the boundary controllability by restriction. In the present paper we give in a first part some direct results of boundary controllability for the hyperbolic Stokes system in a star-shaped domain. We then apply the transmutation method to obtain a result of null controllability for the parabolic Stokes system. One interest is that we can characterize the control that we use and this gives a rather surprising result.