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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II - General Boundary Conditions on Riemannian Manifolds (Hardcover, 1st ed. 2022)
Loot Price: R5,500
Discovery Miles 55 000
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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II - General Boundary Conditions on Riemannian Manifolds (Hardcover, 1st ed. 2022)
Series: PNLDE Subseries in Control, 98
Expected to ship within 10 - 15 working days
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This monograph explores applications of Carleman estimates in the
study of stabilization and controllability properties of partial
differential equations, including quantified unique continuation,
logarithmic stabilization of the wave equation, and
null-controllability of the heat equation. Where the first volume
derived these estimates in regular open sets in Euclidean space and
Dirichlet boundary conditions, here they are extended to Riemannian
manifolds and more general boundary conditions. The book begins
with the study of Lopatinskii-Sapiro boundary conditions for the
Laplace-Beltrami operator, followed by derivation of Carleman
estimates for this operator on Riemannian manifolds. Applications
of Carleman estimates are explored next: quantified unique
continuation issues, a proof of the logarithmic stabilization of
the boundary-damped wave equation, and a spectral inequality with
general boundary conditions to derive the null-controllability
result for the heat equation. Two additional chapters consider some
more advanced results on Carleman estimates. The final part of the
book is devoted to exposition of some necessary background
material: elements of differential and Riemannian geometry, and
Sobolev spaces and Laplace problems on Riemannian manifolds.
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