Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach. (English) Zbl 1417.93067
Summary: Using the backstepping approach we recover the null controllability for the heat equations with variable coefficients in space in one dimension and prove that these equations can be stabilized in finite time by means of periodic time-varying feedback laws. To this end, on the one hand, we provide a new proof of the well-posedness and the “optimal” bound with respect to damping constants for the solutions of the kernel equations; this allows one to deal with variable coefficients, even with a weak regularity of these coefficients. On the other hand, we establish the well-posedness and estimates for the heat equations with a nonlocal boundary condition at one side.
MSC:
| 93B05 | Controllability |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93B17 | Transformations |
| 93B52 | Feedback control |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35K05 | Heat equation |
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