Sidewise profile control of 1-D waves. (English) Zbl 1489.35166
Summary: We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path or profile at the other free end. This sidewise profile control problem is also often referred to as nodal profile or tracking control. The problem is reformulated as a dual observability property for the corresponding adjoint system, which is proved by means of sidewise energy propagation arguments in a sufficiently large time, in the class of BV-coefficients. We also present a number of open problems and perspectives for further research.
MSC:
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 93B05 | Controllability |
| 93B07 | Observability |
Keywords:
1-D wave equations; sidewise profile controllability; nodal profile control; BV-coefficients; sidewise observability; sidewise energy estimatesReferences:
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