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› Find signed collectible books: 'Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems : Proceedings of the 10th International (Lecture Notes in Control & Information Sciences)'
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› Find signed collectible books: 'Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach (Encyclopedia of Mathematics and its Applications)'
This book investigates how a user or observer can influence the behavior of systems mathematically and computationally. A thorough mathematical analysis of controllability problems is combined with a detailed investigation of methods used to solve them numerically; these methods being validated by the results of numerical experiments. In the first part of the book, the authors discuss the mathematics and numerics relating to the controllability of systems modeled by linear and non-linear diffusion equations; Part two is dedicated to the controllability of vibrating systems, typical ones being those modeled by linear wave equations; and finally, part three covers flow control for systems governed by the Navier-Stokes equations modeling incompressible viscous flow. The book is accessible to graduate students in applied and computational mathematics, engineering and physics; it will also be of use to more advanced practitioners.
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› Find signed collectible books: 'Handbook of Numerical Analysis: Numerical Methods for Fluids (Part 3)'
This book-size article is dedicated to the numerical simulation of unsteady incompressible viscous flow modelled by the Navier-Stokes equations, or by non-Newtonian variants of them. In order to achieve this goal a methodology has been developed based on four key tools. Time discretization by operator-splitting schemes such as Peaceman-Rachford's, Douglas Rachford's, Marchuk-Yanenko's, Strang's symmetrized, and the so-called "theta-scheme" introduced by the author in the mid-1980s. Projection methods (in L2 or H1) for the treatment of the incompressibility condition div u = 0. Treatment of the advection by: either a centered scheme leading to linear or nonlinear advection-diffusion problems solved by least squares/conjugate gradient algorithms, or to a linear wave-like equation well suited to finite element-based solution methods. Space approximation by finite element methods such as Hood-Taylor and Bercovier-Pironneau, which are relatively easy to implement. In addition to the above topics the article contains detailed discussions of conjugate gradient algorithms, least-squares methods for boundary-value problems which are not equivalent to problems of the calculus of variations, Uzawa-type algorithms for the solution of saddle-point problems, embedding/fictitious domain methods for the solution of elliptic and parabolic problems. In fact many computational methods discussed in this article also apply to non-CFD problems although they were mostly designed for the solution of flow problems. Among the topics covered are: the direct numerical simulation of particulate flow; computational methods for flow control; splitting methods for viso-plastic flow a la Bingham; and more. It should also be mentioned that most methods discussed in this article are illustrated by the results of numerical experiments, including the simulation of three-dimensional flow. Due to their modularity the methods described in this article are relatively easy to implement - as is demonstrated by the fact that several practitioners in various institutions have been able to use them ab initio for the solution of complicated flow (and other) problems.
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Evolution Problems II'
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Functional and Variational Methods'
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Physical Origins and Classical Methods'
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Spectral Theory and Applications'
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Volume 1 Physical Origins and Classical Methods'
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2 Functional and Variational Methods'
These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and 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. 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. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. 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. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences.
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Volume 3 Spectral Theory and Applications'
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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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Volume 4: Integral Equations'
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Volume 5 Evolution Problems I'
These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and 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. 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. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. 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. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences.
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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Volume 6 Evolution Problems II'
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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› Find signed collectible books: 'Mathematical Analysis and Numerical Methods for Science and Technology: Volume 6: Evolution Problems II (Mathematical analysis & numerical methods for science & technology) (Vol 6)'
These six volumes - the result of a ten year collaboration between the authors, two of France's leading scientists and 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. 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. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to caluclate 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 fact of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences. Volumes 5 and 6 cover problems of Transport and Evolution.
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› Find signed collectible books: 'Non-homogeneous boundary value problems and applications (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen)'
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› Find signed collectible books: 'Non-Homogeneous Boundary Value Problems and Applications: Vol. 1 (Grundlehren der mathematischen Wissenschaften)'
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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› Find signed collectible books: 'Non-Homogeneous Boundary Value Problems and Applications: Vol. 2 (Grundlehren der mathematischen Wissenschaften)'
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› Find signed collectible books: 'Non-Homogeneous Boundary Value Problems and Applications: Vol. 3 (Grundlehren der mathematischen Wissenschaften)'
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› Find signed collectible books: 'Non-Homogeneous Boundary Value Problems and Applications: Volume II (Grundlehren der mathematischen Wissenschaften)'
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 v, where Pis a linear differential operator in m and where the Q/s are linear differential operators on am. In Volumes 1 and 2, we studied, for particular c1asses of systems {P, Qj}, problem (1), (2) in c1asses of Sobolev spaces (in general constructed starting from P) of positive integer or (by interpolation) non-integer order; then, by transposition, in c1asses 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 inlinitely dilferentiable or analytic Itlnctions or of Gevrey-type I~mctions and by duality, in spaces 01 distribtltions, of analytic Itlnctionals or of Gevrey- type ultra-distributions. In this manner, we obtain a c1ear vision (at least we hope so) of the various possible formulations of the boundary value problems (1), (2) for the systems {P, Qj} considered here.
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› Find signed collectible books: 'Nonlinear Partial Differential Equations and Their Applications: Collge de France Seminar Volume XVIII (Chapman & Hall/CRC Research Notes in Mathematics Series) (Vol.13)'
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› Find signed collectible books: 'Nonlinear Partial Differential Equations and Their ApplicationsCollge de France Seminar Volume XI (Chapman & Hall/CRC Research Notes in Mathematics Series)'
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› Find signed collectible books: 'Numerical Analysis of Variational Inequalities (Studies in Mathematics and its Applications, 9)'
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› Find signed collectible books: 'Optimal Control of Systems Governed by Partial Differential Equations (Grundelhren Der Mathematishen Wissenschaften: Vol 170)'
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› Find signed collectible books: 'Proceedings of the China-France Symposium on Finite Element Methods'
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› Find signed collectible books: 'Control of distributed singular systems (French Edition)'
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› Find signed collectible books: 'Controlabilite exacte, perturbations et stabilisation de systemes distribues - tome 2 (French Edition)'
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› Find signed collectible books: 'Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, tome 1. Contrôlabilité exacte (French Edition)'
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› Find signed collectible books: 'Controle des systemes distribues singuliers (Methodes mathematiques de l'informatique) (French Edition)'
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› Find signed collectible books: 'Equations differentielles operationnelles et problemes aux limites (Grundlehren der mathematischen Wissenschaften) (French Edition)'
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› Find signed collectible books: 'Sur quelques questions d'analyse, de mecanique et de controle optimal (Collection de la Chaire Aisenstadt) (French Edition)'
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