Null boundary controllability of a one-dimensional heat equation with an internal point mass and variable coefficients. (English) Zbl 1381.93023
Summary: In this paper, we consider a linear hybrid system which is composed by two non-homogeneous rods connected by a point mass with Dirichlet boundary conditions on the left end and a boundary control acts on the right end. We prove that this system is null controllable with Dirichlet or Neumann boundary controls. Our approach is mainly based on a detailed spectral analysis together with the moment method. In particular, we show that the associated spectral gap in both cases (Dirichlet or Neumann boundary controls) is positive without further conditions on the coefficients other than the regularities.
MSC:
| 93B05 | Controllability |
| 35K05 | Heat equation |
| 45K05 | Integro-partial differential equations |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 93C05 | Linear systems in control theory |
Keywords:
linear hybrid system; non-homogeneous rods; Dirichlet boundary conditions; Dirichlet or Neumann boundary control; null controllability; spectral analysis; moment methodReferences:
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