GUISE
发表于 2025-3-25 06:36:14
Carleman Estimate for a Second-Order Elliptic OperatorConsider a general second-order elliptic operator . with a principal part of the form . where . with all derivatives bounded and such that .. = .., 1 ≤ ., . ≤ .. We recall that . = −.. The elliptic operator under consideration is then . where ., 1 ≤ . ≤ ..
AMITY
发表于 2025-3-25 09:14:11
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Postulate
发表于 2025-3-25 11:59:44
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珠宝
发表于 2025-3-25 18:40:28
Elliptic Operator with Dirichlet Data and Associated SemigroupOn a smooth bounded open set . of ., we consider elliptic second-order operator .. given by . where . with furthermore .. = .., 1 ≤ ., . ≤ .. In addition we shall impose Dirichlet boundary conditions, that is, the trace of the solution at the boundary ..
现代
发表于 2025-3-25 22:40:39
Some Elements of Functional AnalysisHere, . and . will denote Banach spaces with their norms denoted by ∥.∥., ∥.∥., or simply ∥.∥when there is no ambiguity.
几何学家
发表于 2025-3-26 00:12:41
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CARE
发表于 2025-3-26 05:16:14
Book 2022ons, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds..The first three chapters illustrate
艺术
发表于 2025-3-26 10:46:50
Introductionan estimates has gone beyond the original domain; they are also used in the study of stabilization and controllability properties of partial differential equations, two applications we shall consider in this book. Inverse problems are also a field of applications for Carleman estimate; we shall however not touch upon that subject.
HEED
发表于 2025-3-26 13:38:19
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fodlder
发表于 2025-3-26 19:58:57
Controllability of Parabolic Equations, in the time interval (0, .), with homogeneous Dirichlet boundary conditions, and for an initial condition .. in ..(.), is given by . The function . is the control. The goal is to drive the solution . to a prescribe state at time . > 0, yet only acting in the sub-domain .. We shall make precise what can actually be achieved below.