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This brief provides unified methods for the stabilization of some fractional evolution systems, nicely complementing existing literature on fractional calculus. The volume is divided into three chapters, the first of which considers the stabilization for some abstract evolution equations with a fractional damping, the second of which validates the abstract results of chapter 1 on concrete examples, and the third of which studies the stabilization of fractional evolution systems with memory.

Functional analysis --- Differential equations --- Mathematical analysis --- Mathematics --- Classical mechanics. Field theory --- differentiaalvergelijkingen --- analyse (wiskunde) --- mathematische modellen --- dynamica

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Varietats de Riemann --- Problemes de contorn --- Riemannian manifolds. --- Boundary value problems. --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Manifolds, Riemannian --- Riemannian space --- Space, Riemannian --- Geometry, Differential --- Manifolds (Mathematics)

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Riemannian manifolds. --- Boundary value problems. --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Manifolds, Riemannian --- Riemannian space --- Space, Riemannian --- Geometry, Differential --- Manifolds (Mathematics) --- Varietats de Riemann --- Problemes de contorn --- Problemes de valor límit --- Equacions diferencials --- Física matemàtica --- Funcions de variables complexes --- Dispersió (Matemàtica) --- Equacions de Von Kármán --- Problema de Dirichlet --- Problema de Neumann --- Problemes de Riemann-Hilbert --- Problemes de valor inicial --- Espais de Riemann --- Geometria diferencial global --- Teoria del potencial (Matemàtica) --- Varietats de Sasaki

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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.

Algebraic geometry --- Differential geometry. Global analysis --- Operator theory --- Differential equations --- Mathematics --- differentiaalvergelijkingen --- analyse (wiskunde) --- topologie (wiskunde) --- statistiek --- systeemtheorie --- wiskunde --- geometrie