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Author: H.G. Garnir Publisher: Springer Science & Business Media ISBN: 9401012059 Category : Mathematics Languages : en Pages : 484
Book Description
Most of the problems posed by Physics to Mathematical Analysis are boundary value problems for partial differential equations and systems. Among them, the problems concerning linear evolution equations have an outstanding position in the study of the physical world, namely in fluid dynamics, elastodynamics, electromagnetism, plasma physics and so on. This Institute was devoted to these problems. It developed essentially the new methods inspired by Functional Analysis and specially by the theories of Hilbert spaces, distributions and ultradistributions. The lectures brought a detailed exposition of the novelties in this field by world known specialists. We held the Institute at the Sart Tilman Campus of the University of Liege from September 6 to 17, 1976. It was attended by 99 participants, 79 from NATO Countries [Belgium (30), Canada (2), Denmark (I), France (15), West Germany (9), Italy (5), Turkey (3), USA (14)] and 20 from non NATO Countries [Algeria (2), Australia (3), Austria (I), Finland (1), Iran (3), Ireland (I), Japan (6), Poland (1), Sweden (I), Zair (1)]. There were 5 courses of_ 6_ h. ollI'. s~. 1. nL lJ. , h. t;l. l. I. rl"~, 1. n,L ,_ h. t;l. l. I. r. !'~ , ?_ n. f~ ?_ h,,
Author: H.G. Garnir Publisher: Springer Science & Business Media ISBN: 9401012059 Category : Mathematics Languages : en Pages : 484
Book Description
Most of the problems posed by Physics to Mathematical Analysis are boundary value problems for partial differential equations and systems. Among them, the problems concerning linear evolution equations have an outstanding position in the study of the physical world, namely in fluid dynamics, elastodynamics, electromagnetism, plasma physics and so on. This Institute was devoted to these problems. It developed essentially the new methods inspired by Functional Analysis and specially by the theories of Hilbert spaces, distributions and ultradistributions. The lectures brought a detailed exposition of the novelties in this field by world known specialists. We held the Institute at the Sart Tilman Campus of the University of Liege from September 6 to 17, 1976. It was attended by 99 participants, 79 from NATO Countries [Belgium (30), Canada (2), Denmark (I), France (15), West Germany (9), Italy (5), Turkey (3), USA (14)] and 20 from non NATO Countries [Algeria (2), Australia (3), Austria (I), Finland (1), Iran (3), Ireland (I), Japan (6), Poland (1), Sweden (I), Zair (1)]. There were 5 courses of_ 6_ h. ollI'. s~. 1. nL lJ. , h. t;l. l. I. rl"~, 1. n,L ,_ h. t;l. l. I. r. !'~ , ?_ n. f~ ?_ h,,
Author: Athanasios S. Fokas Publisher: SIAM ISBN: 1611973813 Category : Mathematics Languages : en Pages : 290
Book Description
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.? The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Author: Andrea Manzoni Publisher: Springer Nature ISBN: 3030772268 Category : Mathematics Languages : en Pages : 507
Book Description
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Author: Jacques Louis Lions Publisher: Springer Science & Business Media ISBN: 3642651615 Category : Mathematics Languages : en Pages : 375
Book Description
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.
Author: Heinz-Otto Kreiss Publisher: SIAM ISBN: 0898719135 Category : Science Languages : en Pages : 408
Book Description
Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
Author: Mimmo Iannelli Publisher: Birkhäuser ISBN: 3034880855 Category : Mathematics Languages : en Pages : 419
Book Description
The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics. All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.
Author: Jacques Henry Publisher: Elsevier ISBN: 0081010907 Category : Mathematics Languages : en Pages : 258
Book Description
Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems. - Develops the invariant embedding technique for boundary value problems - Makes a link between control theory, boundary value problems and the Gauss factorization - Presents a new theory for successively solving linear elliptic boundary value problems - Includes a transformation in two initial value problems that are uncoupled
Author: Athanasios S. Fokas Publisher: SIAM ISBN: 1611973821 Category : Mathematics Languages : en Pages : 290
Book Description
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs. The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Author: Athanassios S. Fokas Publisher: SIAM ISBN: 0898716519 Category : Mathematics Languages : en Pages : 327
Book Description
A novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.
Author: H.G. Garnir
Author: H.G. Garnir
Author: Athanasios S. Fokas
Author: Athanassios S. Fokas
Author: Andrea Manzoni
Author: Jacques Louis Lions
Author: Heinz-Otto Kreiss
Author: Mimmo Iannelli
Author: Jacques Henry
Author: Athanasios S. Fokas
Author: Athanassios S. Fokas