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<p>This paper considers a semi-discrete forward stochastic parabolic operator with homogeneous Dirichlet conditions in arbitrary dimension. We show the lack of null controllability for a spatial semi-discretization of a null-controllable parabolic system from any initial datum. However, by proving a new Carleman estimate for its semi-discrete backward stochastic adjoint system, we achieve a relaxed observability inequality, which is applied to derivative <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\phi\)</EquationSource> </InlineEquation>-null controllability by duality arguments.</p>

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Carleman Estimate for Semi-discrete Stochastic Parabolic Operators in Arbitrary Dimension and Applications to Controllability

  • 期刊论文

  • 发表日期：

    2025年12月26日

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  • Rodrigo Lecaros,
  • Ariel A. Pérez,
  • Manuel F. Prado

摘要

This paper considers a semi-discrete forward stochastic parabolic operator with homogeneous Dirichlet conditions in arbitrary dimension. We show the lack of null controllability for a spatial semi-discretization of a null-controllable parabolic system from any initial datum. However, by proving a new Carleman estimate for its semi-discrete backward stochastic adjoint system, we achieve a relaxed observability inequality, which is applied to derivative \(\phi\) -null controllability by duality arguments.