Jacques Louis Lions's Books

Non-Homogeneous Boundary Value Problems and Applications

Volume III

By: Jacques Louis Lions,Enrico Magenes

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Non-Homogeneous Boundary Value Problems and Applications

Volume III

By: Jacques Louis Lions,Enrico Magenes

1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1

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323

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Springer Science & Business Media

Published Date

ISBN 10

3642653936

ISBN 13

9783642653933

Mathematical Analysis and Numerical Methods for Science and Technology

Volume 5 Evolution Problems I

By: Robert Dautray,Jacques-Louis Lions

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Mathematical Analysis and Numerical Methods for Science and Technology

Volume 5 Evolution Problems I

By: Robert Dautray,Jacques-Louis Lions

299 G(t), and to obtain the corresponding properties of its Laplace transform (called the resolvent of - A) R(p) = (A + pl)-l , whose existence is linked with the spectrum of A. The functional space framework used will be, for simplicity, a Banach space(3). To summarise, we wish to extend definition (2) for bounded operators A, i.e. G(t) = exp( - tA) , to unbounded operators A over X, where X is now a Banach space. Plan of the Chapter We shall see in this chapter that this enterprise is possible, that it gives us in addition to what is demanded above, some supplementary information in a number of areas: - a new 'explicit' expression of the solution; - the regularity of the solution taking into account some conditions on the given data (u , u1,f etc ... ) with the notion of a strong solution; o - asymptotic properties of the solutions. In order to treat these problems we go through the following stages: in § 1, we shall study the principal properties of operators of semigroups {G(t)} acting in the space X, particularly the existence of an upper exponential bound (in t) of the norm of G(t). In §2, we shall study the functions u E X for which t --+ G(t)u is differentiable.

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760

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Springer Science & Business Media

Published Date

ISBN 10

3540661018

ISBN 13

9783540661016

Mathematical Analysis and Numerical Methods for Science and Technology

Volume 3 Spectral Theory and Applications

By: Robert Dautray,Jacques-Louis Lions

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Mathematical Analysis and Numerical Methods for Science and Technology

Volume 3 Spectral Theory and Applications

By: Robert Dautray,Jacques-Louis Lions

The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. The objective of the present work is to compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form.

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556

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Springer Science & Business Media

Published Date

ISBN 10

3540660992

ISBN 13

9783540660996

Non-Homogeneous Boundary Value Problems and Applications

By: Jacques Louis Lions,Enrico Magenes

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Non-Homogeneous Boundary Value Problems and Applications

By: Jacques Louis Lions,Enrico Magenes

I. In this second volume, we continue at first the study of non homogeneous boundary value problems for particular classes of evolu tion equations. 1 In Chapter 4 , we study parabolic operators by the method of Agranovitch-Vishik [lJ; this is step (i) (Introduction to Volume I, Section 4), i.e. the study of regularity. The next steps: (ii) transposition, (iii) interpolation, are similar in principle to those of Chapter 2, but involve rather considerable additional technical difficulties. In Chapter 5, we study hyperbolic operators or operators well defined in thesense of Petrowski or Schroedinger. Our regularity results (step (i)) seem to be new. Steps (ii) and (iii) are all3.logous to those of the parabolic case, except for certain technical differences. In Chapter 6, the results of Chapter'> 4 and 5 are applied to the study of optimal control problems for systems governed by evolution equations, when the control appears in the boundary conditions (so that non-homogeneous boundary value problems are the basic tool of this theory). Another type of application, to the characterization of "all" well-posed problems for the operators in question, is given in the Ap pendix. Still other applications, for example to numerical analysis, will be given in Volume 3.

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244

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Springer

Published Date

ISBN 10

3540054448

ISBN 13

9783540054443

Mathematical Analysis and Numerical Methods for Science and Technology

Volume 5 Evolution Problems I

By: Robert Dautray,Jacques-Louis Lions

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Mathematical Analysis and Numerical Methods for Science and Technology

Volume 5 Evolution Problems I

By: Robert Dautray,Jacques-Louis Lions

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760

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Springer Science & Business Media

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ISBN 10

3540661018

ISBN 13

9783540661016

Frontiers in Mathematical Analysis and Numerical Methods

In Memory of Jacques-Louis Lions

By: Jacques-Louis Lions,Ta-ch'ien Li,Daqian Li

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Frontiers in Mathematical Analysis and Numerical Methods

In Memory of Jacques-Louis Lions

By: Jacques-Louis Lions,Ta-ch'ien Li,Daqian Li

This invaluable volume is a collection of articles in memory ofJacques-Louis Lions, a leading mathematician and the founder of theContemporary French Applied Mathematics School. The contributions havebeen written by his friends, colleagues and students, including CBardos, A Bensoussan, S S Chern, P G Ciarlet, R Glowinski, Gu Chaohao, B Malgrange, G Marchuk, O Pironneau, W Strauss, R Temam, etc

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316

Publisher

World Scientific

Published Date

ISBN 10

9812562265

ISBN 13

9789812562265

Nonlinear Partial Differential Equations and Their Applications

Collge de France Seminar

By: Doina Cioranescu,Jacques-Louis Lions

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Nonlinear Partial Differential Equations and Their Applications

Collge de France Seminar

By: Doina Cioranescu,Jacques-Louis Lions

This book presents the texts of selected lectures on recent work in the field of nonlinear partial differential equations delivered by leading international experts at the well-established weekly seminar held at the Collège de France. Emphasis is on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis, and engineering. Proceedings of this seminar will be of particular interest to postgraduate students and specialists in the area of nonlinear partial differential equations.

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354

Publisher

CRC Press

Published Date

ISBN 10

0582369266

ISBN 13

9780582369269

Asymptotic Analysis for Periodic Structures

By: Alain Bensoussan,Jacques-Louis Lions,George Papanicolaou

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Asymptotic Analysis for Periodic Structures

By: Alain Bensoussan,Jacques-Louis Lions,George Papanicolaou

This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization. In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.

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410

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853244

ISBN 13

9780821853245

Non-Homogeneous Boundary Value Problems and Applications

By: Jacques Louis Lions,Enrico Magenes

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Non-Homogeneous Boundary Value Problems and Applications

By: Jacques Louis Lions,Enrico Magenes

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.

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360

Publisher

Springer

Published Date

ISBN 10

3540053638

ISBN 13

9783540053637

Continuous Functions

By: Jacques Simon

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Continuous Functions

By: Jacques Simon

This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space. The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers, without restricting or generalizing the results.

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272

Publisher

John Wiley & Sons

Published Date

ISBN 10

1786300109

ISBN 13

9781786300102

Banach, Fréchet, Hilbert and Neumann Spaces

By: Jacques Simon

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Banach, Fréchet, Hilbert and Neumann Spaces

By: Jacques Simon

This book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces. The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers without restricting or generalizing the results.

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368

Publisher

John Wiley & Sons

Published Date

ISBN 10

1119426642

ISBN 13

9781119426646

Distributions

By: Jacques Simon

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Distributions

By: Jacques Simon

This book presents a simple and original theory of distributions, both real and vector, adapted to the study of partial differential equations. It deals with value distributions in a Neumann space, that is, in which any Cauchy suite converges, which encompasses the Banach and Fréchet spaces and the same “weak” spaces. Alongside the usual operations – derivation, product, variable change, variable separation, restriction, extension and regularization – Distributions presents a new operation: weighting. This operation produces properties similar to those of convolution for distributions defined in any open space. Emphasis is placed on the extraction of convergent sub-sequences, the existence and study of primitives and the representation by gradient or by derivatives of continuous functions. Constructive methods are used to make these tools accessible to students and engineers.

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420

Publisher

John Wiley & Sons

Published Date

ISBN 10

1394165358

ISBN 13

9781394165353

Mathematical Analysis and Numerical Methods for Science and Technology

Volume 6 Evolution Problems II

By: Robert Dautray,Jacques-Louis Lions

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Mathematical Analysis and Numerical Methods for Science and Technology

Volume 6 Evolution Problems II

By: Robert Dautray,Jacques-Louis Lions

These six volumes--the result of a ten year collaboration between two distinguished international figures--compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. It is a comprehensive and up-to-date publication that presents the mathematical tools needed in applications of mathematics.

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486

Publisher

Springer

Published Date

ISBN 10

3540661026

ISBN 13

9783540661023

Mathematical Analysis and Numerical Methods for Science and Technology

Volume 1 Physical Origins and Classical Methods

By: Robert Dautray,Jacques-Louis Lions

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Mathematical Analysis and Numerical Methods for Science and Technology

Volume 1 Physical Origins and Classical Methods

By: Robert Dautray,Jacques-Louis Lions

These 6 volumes -- the result of a 10 year collaboration between the authors, both distinguished international figures -- compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. The advent of high-speed computers has made it possible to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way.

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748

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540660976

ISBN 13

9783540660972

Mathematical Analysis and Numerical Methods for Science and Technology

Volume 4 Integral Equations and Numerical Methods

By: Robert Dautray,Jacques-Louis Lions

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Mathematical Analysis and Numerical Methods for Science and Technology

Volume 4 Integral Equations and Numerical Methods

By: Robert Dautray,Jacques-Louis Lions

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493

Publisher

Springer

Published Date

ISBN 10

3642615325

ISBN 13

9783642615320

Book's by Jacques Louis Lions

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

Frontiers in Mathematical Analysis and Numerical Methods

Frontiers in Mathematical Analysis and Numerical Methods

Nonlinear Partial Differential Equations and Their Applications

Nonlinear Partial Differential Equations and Their Applications

Asymptotic Analysis for Periodic Structures

Asymptotic Analysis for Periodic Structures

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

Continuous Functions

Continuous Functions

Banach, Fréchet, Hilbert and Neumann Spaces

Banach, Fréchet, Hilbert and Neumann Spaces

Distributions

Distributions

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

Mathematical Analysis and Numerical Methods for Science and Technology

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