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Research Article Open access CC BY 3.0

Optimal Control Problem for a Modified Novikov Equation with Dissipation

Jiangbo Zhou, Jing Chen, Junde Chen

Archives of Current Research International · pp. 17–27 · Published 3 Jan 2015

10.9734/ACRI/2014/15087

Abstract

This paper investigate the optimal control problem for a modified Novikov equation with dissipation. The existence and uniqueness of regular local solution to the corresponding initial boundary value problem is guaranteed by the Faedo-Galerkin method. A critical estimate of the solution is obtained. Finally, the existence of an optimal solution to the control problem is proved.

Modified Novikov equation optimal control weak solution

References (39)

  1. 1 Infinite-Dimensional Dynamical Systems in Mechanics and Physics [DOI]
  2. 2 An integrable shallow water equation with peaked solitons [DOI]
  3. 3 Optimal Control of Systems Governed by Partial Differential Equations. [DOI]
  4. 4 Introductory functional analysis with applications
  5. 5 Infinite-Dimensional Dynamical Systems in Mechanics and Physics [DOI]
  6. 6 Studies in Mathematics and its Applications [DOI]
  7. 7 Generalizations of the Camassa–Holm equation [DOI]
  8. 8 Integrable peakon equations with cubic nonlinearity [DOI]
  9. 9 Damping of Solitary Waves [DOI]
  10. 10 The Cauchy problem for the Novikov equation [DOI]
  11. 11 Well-posedness and persistence properties for the Novikov equation [DOI]
  12. 12 Global weak solutions for the Novikov equation [DOI]
  13. 13 The Cauchy problem for the integrable Novikov equation [DOI]
  14. 14 Well-posedness and global existence for the Novikov equation [DOI]
  15. 15 Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time [DOI]
  16. 16 Mathematical Analysis and Numerical Methods for Science and Technology [DOI]
  17. 17 Blow-up phenomenon for the integrable Novikov equation [DOI]
  18. 18 Global existence and blow-up phenomena for the weakly dissipative Camassa–Holm equation [DOI]
  19. 19 A Reduced Basis Method for Control Problems Governed by PDEs [DOI]
  20. 20 Optimal Control of Keller–Segel Equations [DOI]
  21. 21 Stability of peakons for the Novikov equation [DOI]
  22. 22 Blow-Up and Decay of the Solution of the Weakly Dissipative Degasperis–Procesi Equation [DOI]
  23. 23 Blow-up, blow-up rate and decay of the solution of the weakly dissipative Camassa-Holm equation [DOI]
  24. 24 Optimal control of the viscous Camassa–Holm equation [DOI]
  25. 25 On the Cauchy problem for the modified Novikov equation with peakon solutions [DOI]
  26. 26 Global existence and blow-up phenomena for the weakly dissipative Novikov equation [DOI]
  27. 27 Optimal Control of Two- and Three-Dimensional Incompressible Navier–Stokes Flows [DOI]
  28. 28 Optimal Control of Stochastic Partial Differential Equations [DOI]
  29. 29 Distributed Control Problems for the Burgers Equation [DOI]
  30. 30 Optimal control of the viscous Degasperis-Procesi equation [DOI]
  31. 31 Optimal control problem for viscous Cahn–Hilliard equation [DOI]
  32. 32 The existence of global strong and weak solutions for the Novikov equation [DOI]
  33. 33 Optimal control of the viscous Dullin–Gottwalld–Holm equation [DOI]
  34. 34 Global existence and blow-up phenomena for a weakly dissipative Degasperis-Procesi equation [DOI]
  35. 35 A course of applied functional analysis
  36. 36 Time-domain decomposition of optimal control problems for the wave equation [DOI]
  37. 37 Optimal Control of the Viscous Burgers Equation Using an Equivalent Index Method [DOI]
  38. 38 A course of applied functional analysis [DOI]
  39. 39 Blow-Up Phenomena and Decay for the Periodic Degasperis-Procesi Equation with Weak Dissipation [DOI]

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