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Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations, Camille Laurent, Matthieu Leautaud


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Автор: Camille Laurent, Matthieu Leautaud
Название:  Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations
ISBN: 9781470451387
Издательство: Mare Nostrum (Eurospan)
Классификация:
ISBN-10: 1470451387
Обложка/Формат: Paperback
Страницы: 95
Вес: 0.20 кг.
Дата издания: 30.06.2022
Серия: Memoirs of the american mathematical society
Язык: English
Размер: 182 x 257 x 24
Ключевые слова: Differential calculus & equations
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Поставляется из: Англии
Описание: This memoir is concerned with quantitative unique continuation estimates for equations involving a sum of squares operator L on a compact manifold M assuming: (i) the Chow-Rashevski-H?ormander condition ensuring the hypoellipticity of L,and(ii) the analyticity of M and the coefficients of L. The first result is the tunneling estimate ?L2(?) ? Ce?c?k 2 for normalized eigenfunctions ? of L from a nonempty open set ? ?M,wherek is the hypoellipticity index of L and ? the eigenvalue. The main result is a stability estimate for solutions to the hypoelliptic wave equation (?2 t + L)u =0:forT>2supx?M(dist(x,?)) (here, dist is the subRiemannian distance), the observation of the solution on (0,T) ? ? determines the data. The constant involved in the estimate is Cec?k where?isthetypical frequency of the data. Wethen prove the approximate controllability of the hypoelliptic heat equation (?t +L)v = 1?f in any time, with appropriate (exponential) cost, depending on k. In case k = 2 (Grushin, Heisenberg...), we further show approximate controllability to trajectories with polynomial cost in large time. We also explain how the a nalyticity assumption can be relaxed, and a boundary ?Mcan be added in some situations.
Дополнительное описание: Differential calculus and equations


Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians

Автор: Gong Chen
Название: Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians
ISBN: 1470449749 ISBN-13(EAN): 9781470449742
Издательство: Mare Nostrum (Eurospan)
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Цена: 71060.00 T
Наличие на складе: Поставка под заказ.
Описание: We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R3:?ttu ? ?u +m j=1 Vj (x ? vj t) u = 0.The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [GC4].

Corrigendum and Improvements to  " "Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations`` and Its Consequences

Автор: Dimitri Mugnai, Genni Fragnelli
Название: Corrigendum and Improvements to " "Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations`` and Its Consequences
ISBN: 1470447878 ISBN-13(EAN): 9781470447878
Издательство: Mare Nostrum (Eurospan)
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Цена: 86850.00 T
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Описание: Acorrigendum and improvements to Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations and its Consequences.

Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems

Автор: Larisa Beilina; Michael Victor Klibanov
Название: Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
ISBN: 1489995307 ISBN-13(EAN): 9781489995308
Издательство: Springer
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Цена: 144410.00 T
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Описание: The first of its kind, this volume presents convergent numerical methods for coefficient inverse problems for partial differential equations. Readers will find globally convergent methods that are synthesized with the Adaptive Finite Element technique (adaptivity for brevity).

Global Carleman Estimates for Degenerate Parabolic Operators with Applications

Автор: P. Cannarsa, P. Martinez, J. Vancostenoble
Название: Global Carleman Estimates for Degenerate Parabolic Operators with Applications
ISBN: 1470414961 ISBN-13(EAN): 9781470414962
Издательство: Mare Nostrum (Eurospan)
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Цена: 99790.00 T
Наличие на складе: Невозможна поставка.
Описание: Introduces the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.

Controllability and Stabilization of Parabolic Equations

Автор: VIOREL BARBU
Название: Controllability and Stabilization of Parabolic Equations
ISBN: 3319766651 ISBN-13(EAN): 9783319766652
Издательство: Springer
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Цена: 93160.00 T
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Описание: This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.

Qualitative Estimates For Partial Differential Equations

Автор: Flavin, J N , Rionero, S.
Название: Qualitative Estimates For Partial Differential Equations
ISBN: 0367448793 ISBN-13(EAN): 9780367448790
Издательство: Taylor&Francis
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Цена: 44910.00 T
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Описание: This book deals with the determination of qualitative estimates for solutions of partial differential equations subject to boundary and/or initial conditions. It is suitable for senior undergraduates, first year postgraduates, and for others contemplating research in partial differential equations.

Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations

Автор: T. Alazard, N. Burq, C. Zuily
Название: Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations
ISBN: 147043203X ISBN-13(EAN): 9781470432034
Издательство: Mare Nostrum (Eurospan)
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Цена: 80390.00 T
Наличие на складе: Невозможна поставка.
Описание: Devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. For two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to $L^2$.

Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations

Автор: Alexander Y. Khapalov
Название: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations
ISBN: 3319868594 ISBN-13(EAN): 9783319868592
Издательство: Springer
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Цена: 46570.00 T
Наличие на складе: Поставка под заказ.
Описание: This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time.

Approximate Analytical Methods for Solving Ordinary Differential Equations

Автор: Radhika, T.S.L , Iyengar, T. , Rani, T.
Название: Approximate Analytical Methods for Solving Ordinary Differential Equations
ISBN: 0367378124 ISBN-13(EAN): 9780367378127
Издательство: Taylor&Francis
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Цена: 65320.00 T
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Описание:

Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.





The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete description of the methods without going deep into rigorous mathematical aspects. Detailed examples illustrate the application of the methods to solve real-world problems.





The authors introduce the classical power series method for solving differential equations before moving on to asymptotic methods. They next show how perturbation methods are used to understand physical phenomena whose mathematical formulation involves a perturbation parameter and explain how the multiple-scale technique solves problems whose solution cannot be completely described on a single timescale. They then describe the Wentzel, Kramers, and Brillown (WKB) method that helps solve both problems that oscillate rapidly and problems that have a sudden change in the behavior of the solution function at a point in the interval. The book concludes with recent nonperturbation methods that provide solutions to a much wider class of problems and recent analytical methods based on the concept of homotopy of topology.


Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations

Автор: Alexander Y. Khapalov
Название: Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations
ISBN: 3319604139 ISBN-13(EAN): 9783319604138
Издательство: Springer
Рейтинг:
Цена: 93160.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time.

Controllability and Stabilization of Parabolic Equations

Автор: Viorel Barbu
Название: Controllability and Stabilization of Parabolic Equations
ISBN: 3030095509 ISBN-13(EAN): 9783030095505
Издательство: Springer
Рейтинг:
Цена: 93160.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.


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