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Control of Heat Equations

Salimi, Leila | 2012

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 43386 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Fotouhi Firouzabad, Morteza
  7. Abstract:
  8. The controllability problem may be formulated roughly as follows. Consider an evolution system (either described in terms of partial or ordinary differential equations) on which we are allowed to act by means of a suitable choice of the control (the right-hand side of the system, the boundary conditions, etc.). Given a time interval 0 < t < T, and initial and final states, the goal is to determine whether there exists a control driving the given initial data to the given final ones in time T. Now, consider the simplest parabolic equation, namely heat equation and suppose that one could act by appropraite controls on this system. The null controllability problem which is one of the very important problems in the control system, investigate that if there is a control that by starting from the initial data, get the system to the equilibrium point? But, in application, many problems could be described by the degenerate parabolic equations that the degeneracy occured in the boundary of the domain. In this thesis, we investigate the null controllability for a class of one dimensional degenerate/singular parabolic equations . For this reason we derive a estimate for the solutions of the adjoint problem whose proof is based on the improved Hardy inequality. Also, the results in this thesis improves some recent results on the null controllability of parabolic equations.
  9. Keywords:
  10. Hardy Inequality ; Null Controllability ; Singular Parabolic Equation ; Degenerate Parabolic Equation ; Degenerate/Singular Parabolic Equation ; Carleman Estimate

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