Local Boundary Controllability in Classes of Differentiable Functions for the Wave Equation

@article{Belishev2017LocalBC,
  title={Local Boundary Controllability in Classes of Differentiable Functions for the Wave Equation},
  author={Mikhail I. Belishev},
  journal={Journal of Mathematical Sciences},
  year={2017},
  volume={238},
  pages={591-600}
}
  • M. Belishev
  • Published 3 August 2017
  • Mathematics
  • Journal of Mathematical Sciences
The well-known fact following from the Holmgren-John-Tataru uniqueness theorem is a local approximate boundary L2-controllability of the dynamical system governed by the wave equation. Generalizing this result, we establish the controllability in certain classes of differentiable functions in the domains filled up with waves. 

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References

SHOWING 1-10 OF 14 REFERENCES

Boundary Value Control Theory of the Higher-Dimensional Wave Equation, Part II

The present work extends controllability results obtained for the wave equation in two or more space variables in an earlier article [13]. In the earlier paper approximate controllability was

Recent progress in the boundary control method

The review covers the period 1997–2007 of development of the boundary control method, which is an approach to inverse problems based on their relations to control theory (Belishev 1986). The method

TOPICAL REVIEW: Boundary control in reconstruction of manifolds and metrics (the BC method)

One of the approaches to inverse problems based upon their relations to boundary control theory (the so-called BC method) is presented. The method gives an efficient way to reconstruct a Riemannian

Unique continuation for solutions to pde's; between hörmander's theorem and holmgren' theorem

We prove a new unique continuation result for solutions to partial differential equations, “interpolating” between Holmgren's Theorem and Hormander's Theorem. More precisely, under some partial

Non homogeneous boundary value problems for second order hyperbolic operators

Soit A(x,t) un operateur elliptique d'ordre 2 sur Ω ouvert borne de R n a frontiere Γ lisse. On etudie des problemes de regularite sur un intervalle fini [0,T], T<∞ du probleme hyperbolique d'ordre 2

Spectral theory : self adjoint operators in Hilbert space

B-algebras. Bounded Normal Operators in Hilbert Space. Miscellaneous Operators in Hilbert Space. Unbounded Operators in Hilbert Space. Ordinary Differential Operators. Linear Partial Differential

Spectral Theory of Self-Adjoint Operators in Hilbert Space

1. Preliminaries.- 1. Metric Spaces. Normed Spaces.- 2. Algebras and ?-Algebras of Sets.- 3. Countably Additive Functions and Measures.- 4. Measurable Functions.- 5. Integration.- 6. Function

Recent Advances in Regularity of Second-order Hyperbolic Mixed Problems, and Applications

The present paper centers on second-order hyperbolic equations in the unknownw(t,x): $${w_{tt}} + A(x,\partial )w = f{\text{ in }}\Omega =(0,T]x\Omega $$ (1.1) augmented by initial

Local boundary controllability in smooth classes of functions for the wave equation

  • PDMI PREPRINT – 1/1997,
  • 1997