A Unified Boundary Controllability Theory for Hyperbolic and Parabolic Partial Differential Equations
Author:
- 1 September 1973
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 52 (3) , 189-211
Abstract
With use of the method of spherical means we are able to show that control processes modelled by the wave equation in a domain Ω ⊆ Rn are exactly controllable in finite time by control forces applied at the boundary of the spatial region Ω. The introduction of certain concepts from harmonic analysis together with use of the Fourier transform enables us to apply this result to obtain finite time exact controllability theorems for processes modelled by the heat equation in the same region Ω with controls of the same type.Keywords
This publication has 7 references indexed in Scilit:
- Control theory of hyperbolic equations related to certain questions in harmonic analysis and spectral theoryJournal of Mathematical Analysis and Applications, 1972
- Boundary Value Control of the Higher-Dimensional Wave EquationSIAM Journal on Control, 1971
- Exact controllability theorems for linear parabolic equations in one space dimensionArchive for Rational Mechanics and Analysis, 1971
- On the controllability of distributed parameter systems†International Journal of Control, 1970
- Elementary remarks on completenessDuke Mathematical Journal, 1968
- Nonharmonic Fourier series in the control theory of distributed parameter systemsJournal of Mathematical Analysis and Applications, 1967
- On linear partial differential equations with analytic coefficients unique continuation of dataCommunications on Pure and Applied Mathematics, 1949