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Non Homogeneous Boundary Value Problems And Applications
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Book Synopsis Non-Homogeneous Boundary Value Problems and Applications by : Jacques Louis Lions
Download or read book Non-Homogeneous Boundary Value Problems and Applications written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-homogeneous boundary value problems and applications by : J. L. Lions
Download or read book Non-homogeneous boundary value problems and applications written by J. L. Lions and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Homogeneous Boundary Value Problems and Applications by : Jacques-Louis Lions
Download or read book Non-Homogeneous Boundary Value Problems and Applications written by Jacques-Louis Lions and published by . This book was released on 2014-09-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Homogeneous Boundary Value Problems and Applications by : Jacques Louis Lions
Download or read book Non-Homogeneous Boundary Value Problems and Applications written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-homogeneous boundary value problems and applications by : J. L. Lions
Download or read book Non-homogeneous boundary value problems and applications written by J. L. Lions and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-homogeneous Boundary Value Problems and Applications [by] J.L. Lions [and] E. Magenes by : Jacques Louis Lions
Download or read book Non-homogeneous Boundary Value Problems and Applications [by] J.L. Lions [and] E. Magenes written by Jacques Louis Lions and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Homogeneous Boundary Value Problems and Applications by : Jacques Louis Lions
Download or read book Non-Homogeneous Boundary Value Problems and Applications written by Jacques Louis Lions and published by Springer. This book was released on 2011-11-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis NON HOMOGENEOUS BOUNDARY VALUE PROBLEMS AND APPLICATIONS [Vol 1-3]. by : JL. LIONS
Download or read book NON HOMOGENEOUS BOUNDARY VALUE PROBLEMS AND APPLICATIONS [Vol 1-3]. written by JL. LIONS and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis NON HOMOGENEOUS BOUNDARY VALUE PROBLEMS AND APPLICATIONS [Vol 1-3]. by : J. L. Lions
Download or read book NON HOMOGENEOUS BOUNDARY VALUE PROBLEMS AND APPLICATIONS [Vol 1-3]. written by J. L. Lions and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-homogeneous Boundary Value Problems and Applications by : Jacques-Louis Lions
Download or read book Non-homogeneous Boundary Value Problems and Applications written by Jacques-Louis Lions and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-homogeneous boundary value problems and applications (Problèmes aux limites non homogènes et applications, engl.) Transl. from the French by P. Kenneth by : Jacques Louis Lions
Download or read book Non-homogeneous boundary value problems and applications (Problèmes aux limites non homogènes et applications, engl.) Transl. from the French by P. Kenneth written by Jacques Louis Lions and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-homogeneous Boundary Value Problems and Applications: Die Grund. der Math. Wiss. in Einzel., 183 by : Jacques-Louis Lions
Download or read book Non-homogeneous Boundary Value Problems and Applications: Die Grund. der Math. Wiss. in Einzel., 183 written by Jacques-Louis Lions and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations and Boundary-Value Problems with Applications by : Mark A. Pinsky
Download or read book Partial Differential Equations and Boundary-Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Book Synopsis Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems by : Dumitru Motreanu
Download or read book Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems written by Dumitru Motreanu and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.
Book Synopsis Numerical Solution of Nonlinear Boundary Value Problems with Applications by : Milan Kubicek
Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubicek and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.
Book Synopsis Boundary Value Problems by : F. D. Gakhov
Download or read book Boundary Value Problems written by F. D. Gakhov and published by Elsevier. This book was released on 2014-07-10 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.
Book Synopsis Boundary Value Problems by : Andrew George Mackie
Download or read book Boundary Value Problems written by Andrew George Mackie and published by . This book was released on 1989 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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