Non Homogeneous Boundary Value Problems And Applications By J L Lions And E Magenes
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Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In Volumes 1 and 2, we studied, for particular classes of systems {[capital italic]P, [capital italic]Q[lowercase italic subscript]j}, problems in classes of Sobolev spaces (in general constructed starting from [capital italic]L2) of positive integer or (by interpolation) non-integer order; then, by transposition, in classes of Sobolev spaces of negative order, until, by passage to the limit on the order, we reached the spaces of distributions of finite order. In this volume, we study the analogous problems in spaces of infinitely differentiable or analytic functions or of Gevrey-type functions and by duality, in spaces of distributions, of analytic functionals or of Gevrey-type ultra-distributions. In this manner, we obtain a clear vision (at least we hope so) of the various possible formulations of the boundary value problems for the systems {[capital italic]P, [capital italic]Q[lowercase italic subscript]j} considered here.
Non Homogeneous Boundary Value Problems And Applications By J L Lions And E Magenes
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Author : Jacques Louis Lions
language : en
Publisher:
Release Date : 1972
Non Homogeneous Boundary Value Problems And Applications By J L Lions And E Magenes written by Jacques Louis Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Boundary value problems categories.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
Non Homogeneous Boundary Value Problems And Applications
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Author : J. L. Lions
language : de
Publisher:
Release Date : 1972
Non Homogeneous Boundary Value Problems And Applications written by J. L. Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Several Complex Variables
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Author : Michael Schneider
language : en
Publisher: Cambridge University Press
Release Date : 1999
Several Complex Variables written by Michael Schneider and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.
Analysis And Numerics Of Partial Differential Equations
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Author : Franco Brezzi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-22
Analysis And Numerics Of Partial Differential Equations written by Franco Brezzi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-22 with Mathematics categories.
This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.
Linear And Quasi Linear Evolution Equations In Hilbert Spaces
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Author : Pascal Cherrier
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-14
Linear And Quasi Linear Evolution Equations In Hilbert Spaces written by Pascal Cherrier and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-14 with Mathematics categories.
This book considers evolution equations of hyperbolic and parabolic type. These equations are studied from a common point of view, using elementary methods, such as that of energy estimates, which prove to be quite versatile. The authors emphasize the Cauchy problem and present a unified theory for the treatment of these equations. In particular, they provide local and global existence results, as well as strong well-posedness and asymptotic behavior results for the Cauchy problem for quasi-linear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasi-linear equations, by means of a linearization and fixed-point technique. The authors also compare hyperbolic and parabolic problems, both in terms of singular perturbations, on compact time intervals, and asymptotically, in terms of the diffusion phenomenon, with new results on decay estimates for strong solutions of homogeneous quasi-linear equations of each type. This textbook presents a valuable introduction to topics in the theory of evolution equations, suitable for advanced graduate students. The exposition is largely self-contained. The initial chapter reviews the essential material from functional analysis. New ideas are introduced along with their context. Proofs are detailed and carefully presented. The book concludes with a chapter on applications of the theory to Maxwell's equations and von Karman's equations.
Introduction To The Calculus Of Variations And Control With Modern Applications
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Author : John A. Burns
language : en
Publisher: CRC Press
Release Date : 2013-08-28
Introduction To The Calculus Of Variations And Control With Modern Applications written by John A. Burns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-28 with Mathematics categories.
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.
Recent Advances On Elliptic And Parabolic Issues
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Author : Michel Chipot
language : en
Publisher: World Scientific
Release Date : 2006
Recent Advances On Elliptic And Parabolic Issues written by Michel Chipot and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume is a collection of articles discussing the most recent advances on various topics in partial differential equations. Many important issues regarding evolution problems, their asymptotic behavior and their qualitative properties are addressed. The quality and completeness of the articles will make this book a source of inspiration and references in the future. Contents: Steady Free Convection in a Bounded and Saturated Porous Medium (S Akesbi et al.); Quasilinear Parabolic Functional Evolution Equations (H Amann); A Linear Parabolic Problem with Non-Dissipative Dynamical Boundary Conditions (C Bandle & W Reichel); Remarks on Some Class of Nonlocal Elliptic Problems (M Chipot); On Some Definitions and Properties of Generalized Convex Sets Arising in the Calculus of Variations (B Dacorogna et al.); Note on the Asymptotic Behavior of Solutions to an Anisotropic Crystalline Curvature Flow (C Hirota et al.); A Reaction-Diffusion Approximation to a Cross-Diffusion System (M Iida et al.); Bifurcation Diagrams to an Elliptic Equation Involving the Critical Sobolev Exponent with the Robin Condition (Y Kabeya); Ginzburg-Landau Functional in a Thin Loop and Local Minimizers (S Kosugi & Y Morita); Singular Limit for Some Reaction Diffusion System (K Nakashima); Rayleigh-B(r)nard Convection in a Rectangular Domain (T Ogawa & T Okuda); Some Convergence Results for Elliptic Problems with Periodic Data (Y Xie); On Global Unbounded Solutions for a Semilinear Parabolic Equation (E Yanagida). Readership: Graduate students and researchers in partial differential equations and nonlinear science.
Advances In Solid And Fracture Mechanics
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Author : Holm Altenbach
language : en
Publisher: Springer Nature
Release Date : 2022-11-08
Advances In Solid And Fracture Mechanics written by Holm Altenbach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-08 with Technology & Engineering categories.
This book presents a collection of articles reporting the current challenges in solid and fracture mechanics. The book is devoted to the 90th birthday of academician Nikita F. Morozov—a well-known specialist in the field of solid and fracture mechanics.