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A Unified Boundary Controllability Theory for Hyperbolic and Parabolic Partial Differential Equations
Author(s) -
Russell David L.
Publication year - 1973
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1973523189
Subject(s) - controllability , partial differential equation , mathematics , mathematical analysis , hyperbolic partial differential equation , heat equation , boundary (topology) , wave equation , fourier transform , parabolic partial differential equation , domain (mathematical analysis) , boundary value problem , harmonic , physics , quantum mechanics
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 ⊆ R n 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.