Inverse Source Problem for the Stokes System

  • Oleg Yu Imanuvilov
  • Masahiro Yamamoto
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 5)

Abstract

We consider a Stokes system with external force term:
$$\frac{{\partial y}}{{\partial t}} = \Delta y - \nabla p + r\left( t \right)f\left( x \right),\nabla \cdot y = 0in\left( {0,T} \right) \times \Omega $$
and
$${y_{\left| {\left( {0,T} \right) \times \partial \Omega } \right.}} = 0,$$
where Ω ⊂ ℝ n , n = 2,3 is a bounded domain. We discuss an inverse source problem of determining f = (f 1,..., f n ) from \({y_{\left| {\omega \times \left( {0,T} \right)} \right.}},{p_{\left| {\omega \times \left( {0,T} \right)} \right.}},y\left( {\theta ,\cdot } \right)\) and p(θ, ·), provided that ω ⊂Ω is an arbitrary domain, θ >0 and real-valued r are given. Our main result is the Lipschitz stability in the inverse problem and the proof is based on a Carleman estimate for the Stokes system.

Keywords

Inverse Problem Parabolic Equation Stokes System Exact Controllability Carleman Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Oleg Yu Imanuvilov
    • 1
  • Masahiro Yamamoto
    • 2
  1. 1.Korean Institute for Advanced StudySeoulKorea
  2. 2.Department of Mathematical SciencesThe University of TokyoTokyo 153Japan

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