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Semigroup methods and approximation of nonlinear parabolic boundary control problems

  • Optimal Control
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System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 143))

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References

  1. ALT, W.: On the approximation of infinite optimization problems with an application to optimal control. Appl. Math. Opt. 12 (1984), 15–27.

    Google Scholar 

  2. AMANN, H.: Parabolic evolution equations with nonlinear boundary conditions. J. Differential Equations 72 (1988), 201–269.

    Google Scholar 

  3. FATTORINI, H.O.: Boundary control systems. SIAM J. Control Optimization 6 (1968), 349–385.

    Google Scholar 

  4. FATTORINI, H.O.: A unified theory of necessary conditions for nonlinear nonconvex control systems. Appl. Math. Optimization 15 (1987), 141–185.

    Google Scholar 

  5. GOLDBERG, H. and F. TRÖLTZSCH: Second order optimality conditions for a class of control problems governed by nonlinear integral equations with application to parabolic boundary control. Optimization 20 (1989), 687–698.

    Google Scholar 

  6. LASIECKA, I.: Boundary control of parabolic systems: finite-element approximation. Appl. Math. Optimization 6 (1980). 31–62.

    Google Scholar 

  7. LASIECKA, I.: Galerkin approximation of abstract parabolic boundary value problems with rough boundary data-LP-theory. Math. of Computation 47 (1986), 55–75.

    Google Scholar 

  8. LASIECKA, I.: Stabilization of hyperbolic and parabolic systems with nonlinear perturbed boundary conditions. J. Diff. Equations 75 (1988), 53–87.

    Google Scholar 

  9. TRÖLTZSCH, F.: On the semigroup approach for the optimal control of semilinear parabolic equations including distributed and boundary control. Z. Anal. Anwendungen 8 (1989)

    Google Scholar 

  10. TRÖLTZSCH, F.: On convergence of semidiscrete Ritz-Galerkin schemes applied to the boundary control of parabolic equations with nonlinear boundary condition. To appear in ZAMM.

    Google Scholar 

  11. TRÖLTZSCH, F.: Approximation of non-linear parabolic boundary control problems by the Fourier method — convergence of optimal controls. To appear in Optimization.

    Google Scholar 

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H. -J. Sebastian K. Tammer

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© 1990 International Federation for Information Processing

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Tröltzsch, F. (1990). Semigroup methods and approximation of nonlinear parabolic boundary control problems. In: Sebastian, H.J., Tammer, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008394

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  • DOI: https://doi.org/10.1007/BFb0008394

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52659-9

  • Online ISBN: 978-3-540-47095-3

  • eBook Packages: Springer Book Archive

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