Skip to main content

Shape sensitivity analysis for stochastic evolution equations

  • Conference paper
  • First Online:
Boundary Control and Boundary Variation

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 178))

  • 191 Accesses

Abstract

Shape differential stability of the solutions to stochastic partial differential equations is shown. Parabolic and hyperbolic stochastic PDE's are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.A. Adams, Sobolev Spaces. Academic Press, New York, 1975

    Google Scholar 

  2. A. Bensoussan and B. Viot, Optimal control of stochastic linear distributed systems, SIAM J. Control and Optimization 13 1975 p.904–926

    Google Scholar 

  3. A. Bensoussan, Methodes de Perturbation en Controle Stochastique, Dunod, Paris 1988

    Google Scholar 

  4. G. Da Prato, S. Kwapień and J. Zabczyk, Regularity of solutions of linear stochastic equations in Hilbert spaces, Stochastics 23 1987 p.1–23

    Google Scholar 

  5. D. Gatarek, On convergence of deterministic and stochastic hyperbolic equations, Bolletino dell Unione Matematica Itatiana (in press)

    Google Scholar 

  6. D. Gatarek and J. Sokołowski, Shape sensitivity analysis of optimal control problems for stochastic parabolic equations. Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos, Octubre 1990, editado por: Grupo de Analisis Matematico Aplicado de la Universidad de Malaga. 1991 p.103–114.

    Google Scholar 

  7. I. Lasiecka, J. Sokołowski, Sensitivity analysis of control constrained optimal control problem for wave equation. SIAM Journal on Control and Optimization 29 1991 (in press)

    Google Scholar 

  8. J.L. Lions and E. Magenes, Problemes aux limites non homogenes. Dunod, Paris, 1968

    Google Scholar 

  9. M. Metivier, Semimartingales, a Course on Stochastic Processes, de Gruyter, Berlin 1982

    Google Scholar 

  10. E. Pardoux, Equations aux Derivees Partielles Stochastiques non Lineaires Monotonnes, Thesis, Universite Paris IX, 1975

    Google Scholar 

  11. J. Sokołowski, Shape sensitivity analysis of boundary optimal control problems for parabolic systems. SIAM Journal on Control and Optimization. 26 1988 p.763–787.

    Google Scholar 

  12. J. Sokołowski and J.P. Zolesio, Shape sensitivity analysis of unilateral problems. SIAM J. Math. Anal. 18 1987 p.1416–1437

    Google Scholar 

  13. J. Sokołowski and J.P. Zolesio, Introduction to shape optimization. Shape sensitivity analysis. Springer 1991 (in press).

    Google Scholar 

  14. J.P. Zolesio, The material derivative (or speed) method for shape optimization. In: Optimization of Distributed Parameter Structures, E.J. Haug and J. Cea (Eds.) Sijthoff and Noordhoff, 1981 p.1089–1151

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jean Paul Zoléesio

Rights and permissions

Reprints and permissions

Copyright information

© 1992 International Federation for Information Processing

About this paper

Cite this paper

Gatarek, D., Sokołowski, J. (1992). Shape sensitivity analysis for stochastic evolution equations. In: Zoléesio, J.P. (eds) Boundary Control and Boundary Variation. Lecture Notes in Control and Information Sciences, vol 178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006697

Download citation

  • DOI: https://doi.org/10.1007/BFb0006697

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55351-9

  • Online ISBN: 978-3-540-47029-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics