Qualitative Estimates For Partial Differential Equations, Rionero, S.
Автор: Oksendal Название: Stochastic Differential Equations ISBN: 3540047581 ISBN-13(EAN): 9783540047582 Издательство: Springer Рейтинг: Цена: 54820.00 T Наличие на складе: Есть Описание: Gives an introduction to the basic theory of stochastic calculus and its applications. This book offers examples in order to motivate and illustrate the theory and show its importance for many applications in for example economics, biology and physics.
Автор: Camille Laurent, Matthieu Leautaud Название: Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations ISBN: 1470451387 ISBN-13(EAN): 9781470451387 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 71060.00 T Наличие на складе: Поставка под заказ. 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.
Автор: R. M. M. Mattheij Название: Partial Differential Equations ISBN: 0898715946 ISBN-13(EAN): 9780898715941 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 142120.00 T Наличие на складе: Поставка под заказ. Описание: Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.
Автор: Gong Chen Название: Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians ISBN: 1470449749 ISBN-13(EAN): 9781470449742 Издательство: Mare Nostrum (Eurospan) Рейтинг: 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].
Автор: Feruccio Colombini; Claude Zuily Название: Carleman Estimates and Applications to Uniqueness and Control Theory ISBN: 0817642307 ISBN-13(EAN): 9780817642303 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Consists of 14 research articles that are an outgrowth of a scientific meeting held in Cortona on the subject of Carleman Estimates and Control Theory. This volume includes topics such as unique continuation for elliptic PDEs and systems, control theory and inverse problems. It is suitable for researchers and graduate students of pdes.
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) Рейтинг: 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.
Автор: Feruccio Colombini; Claude Zuily Название: Carleman Estimates and Applications to Uniqueness and Control Theory ISBN: 1461266602 ISBN-13(EAN): 9781461266600 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The articles in this volume reflect a subsequent development after a scientific meeting entitled Carleman Estimates and Control Theory, held in Cartona in September 1999. The 14 research-level articles, written by experts, focus on new results on Carleman estimates and their applications to uniqueness and controlla- bility of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, con- trol theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory. the reader will find applications of Carleman estimates to stabiliza- tion, observability and exact control for the wave and the SchrOdinger equations. A final paper presents a challenging list of open problems on the topic of control- lability of linear and sernilinear heat equations. The papers contain exhaustive and essentially self-contained proofs directly ac- cessible to mathematicians, physicists, and graduate students with an elementary background in PDEs. Contributors are L. Aloui, M. Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M. Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji, K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E. Zuazua.
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) Рейтинг: 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 $L^2$.
Автор: Xiaoyu Fu; Qi L?; Xu Zhang Название: Carleman Estimates for Second Order Partial Differential Operators and Applications ISBN: 303029529X ISBN-13(EAN): 9783030295295 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.
Автор: Igor W. Gel`man Название: Estimates for Differential Operators in Half-space ISBN: 3037191910 ISBN-13(EAN): 9783037191910 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 60060.00 T Наличие на складе: Поставка под заказ.
Автор: Michael Ruzhansky; Mitsuru Sugimoto; Jens Wirth Название: Evolution Equations of Hyperbolic and Schr?dinger Type ISBN: 303480802X ISBN-13(EAN): 9783034808026 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area.
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