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Author: Valeri Agoshkov
Publisher: Springer Science & Business Media
ISBN: 1461219949
Category : Mathematics
Languages : en
Pages : 295
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Book Description
In the modern theory of boundary value problems the following ap proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].
Author: Valeri Agoshkov
Publisher: Springer Science & Business Media
ISBN: 9780817639860
Category : Mathematics
Languages : en
Pages : 304
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Book Description
In the modern theory of boundary value problems the following ap proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].
Author: Valeri Agoshkov
Publisher: Springer Science & Business Media
ISBN: 1461219949
Category : Mathematics
Languages : en
Pages : 295
Get Book Here
Book Description
In the modern theory of boundary value problems the following ap proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].
Author: A.S. Yakimov
Publisher: Academic Press
ISBN: 0128043636
Category : Mathematics
Languages : en
Pages : 202
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Book Description
Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. - Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers - Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series - Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation - Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies - Features extensive revisions from the Russian original, with 115+ new pages of new textual content
Author: Jian-Ke Lu
Publisher: World Scientific
ISBN: 9789810210205
Category : Mathematics
Languages : en
Pages : 484
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Book Description
This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincar-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter I describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals; Chapters II and III study, respectively, fundamental boundary value problems and their applications to singular integral equations for closed contours; Chapters IV and V discuss the same problems for curves with nodes (including open arcs); Chaper VI deals with similar problems for systems of functions; Chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of these exercises.For graduate students or seniors, all the 7 chapters can be used for a full year course, while the first 3 chapters may be used for a one-semester course.
Author: Valeri Agoshkov
Publisher:
ISBN: 9781461219958
Category :
Languages : en
Pages : 300
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Book Description
Author: Charles Henry Edwards
Publisher: Pearson
ISBN: 9780321796981
Category : Boundary value problems
Languages : en
Pages : 0
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Book Description
Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies.
Author: Kenneth J. Beers
Publisher: Cambridge University Press
ISBN: 9780521859714
Category : Computers
Languages : en
Pages : 496
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Book Description
Applications of numerical mathematics and scientific computing to chemical engineering.
Author: Dennis G. Zill
Publisher:
ISBN: 9780534420741
Category : Boundary value problems
Languages : en
Pages : 619
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Book Description
Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the "how" behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.
Author: Olʹga A. Ladyženskaja
Publisher: American Mathematical Soc.
ISBN: 9780821830109
Category : Boundary value problems
Languages : en
Pages : 218
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Book Description
Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
