{"product_id":"elliptic-carleman-estimates-and-applications-to-stabilization-and-controllability-volume-i-dirichlet-boundary-conditions-on-euclidean-space-9783030886769","title":"Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I: Dirichlet Boundary Conditions on Euclidean Space","description":"\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003eThis monograph discusses Carleman estimates' applications to studying the stabilization and controllability properties of partial differential equations, including the damped wave equation and the heat equation. It derives Carleman estimates using pseudo-differential calculus with a large parameter and addresses continuation issues, proving the logarithmic stabilization of the damped wave equation. \u003c\/blockquote\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 411 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 30 March 2023\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer Nature Switzerland AG\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis monograph delves into the realm of Carleman estimates, exploring their applications in the study of stabilization and controllability properties of partial differential equations. It encompasses various topics, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. The analysis is conducted within the framework of open sets in Euclidean space, with plans to extend this treatment to Riemannian manifolds in a future volume.\u003cbr\u003e\u003cbr\u003eThe first three chapters provide a comprehensive derivation of Carleman estimates utilizing pseudo-differential calculus with a large parameter. Subsequently, continuation issues are addressed, leading to a proof of the logarithmic stabilization of the damped wave equation through two alternative approaches of the resolvent estimate for the generator of a damped wave semigroup. The authors then delve into the null-controllability of the heat equation, discussing its equivalence with observability, and how the spectral inequality facilitates the construction of control functions or the establishment of observability inequalities.\u003cbr\u003e\u003cbr\u003eThe final section of the book focuses on presenting essential background material, encompassing the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data, and various elements from functional analysis and semigroup theory. This comprehensive treatment offers a thorough exploration of the applications of Carleman estimates in the field of partial differential equations, providing valuable insights for researchers and practitioners alike.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 795g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 254 x 178 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783030886769\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2022\u003c\/p\u003e","brand":"Jerome Le Rousseau,Gilles Lebeau,Luc Robbiano","offers":[{"title":"Paperback \/ softback","offer_id":44307629965562,"sku":"9783030886769","price":99.95,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/noImage_1_7743d0e1-0833-4aa2-815a-0ba0a5ce02cb.jpg?v=1688110642","url":"https:\/\/shulphink.com\/products\/elliptic-carleman-estimates-and-applications-to-stabilization-and-controllability-volume-i-dirichlet-boundary-conditions-on-euclidean-space-9783030886769","provider":"Shulph Ink","version":"1.0","type":"link"}