Theory Of Singular Boundary Value Problems
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| Author | : Donal O'regan |
| Publisher | : World Scientific |
| Total Pages | : 173 |
| Release | : 1994-04-29 |
| Genre | : Mathematics |
| ISBN | : 9814502006 |
Download Theory Of Singular Boundary Value Problems Book in PDF, Epub and Kindle
This book surveys some topics in the rapidly developing areas of regular and singular boundary value problems. It also provides a detailed account of the current state of the literature on existence theory for ordinary differential equations. Results are presented for finite and semi-infinite intervals. Singularities in both independent and dependent variables are discussed.
| Author | : N. I. Muskhelishvili |
| Publisher | : Courier Corporation |
| Total Pages | : 466 |
| Release | : 2013-02-19 |
| Genre | : Mathematics |
| ISBN | : 0486145069 |
Download Singular Integral Equations Book in PDF, Epub and Kindle
DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div
| Author | : E.M. de Jager |
| Publisher | : Elsevier |
| Total Pages | : 353 |
| Release | : 1996-11-08 |
| Genre | : Mathematics |
| ISBN | : 0080542751 |
Download The Theory of Singular Perturbations Book in PDF, Epub and Kindle
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathematical justification of these methods. The latter implies a priori estimates of solutions of differential equations; this involves the application of Gronwall's lemma, maximum principles, energy integrals, fixed point theorems and Gåding's theorem for general elliptic equations. These features make the book of value to mathematicians and researchers in the engineering sciences, interested in the mathematical justification of formal approximations of solutions of practical perturbation problems. The text is selfcontained and each chapter is concluded with some exercises.
| Author | : F. D. Gakhov |
| Publisher | : Elsevier |
| Total Pages | : 585 |
| Release | : 2014-07-10 |
| Genre | : Mathematics |
| ISBN | : 1483164985 |
Download Boundary Value Problems Book in PDF, Epub and Kindle
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.
| Author | : Georgii S Litvinchuk |
| Publisher | : |
| Total Pages | : 402 |
| Release | : 2000-09-30 |
| Genre | : |
| ISBN | : 9789401143646 |
Download Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift Book in PDF, Epub and Kindle
| Author | : Ferdinand Verhulst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 332 |
| Release | : 2006-06-04 |
| Genre | : Mathematics |
| ISBN | : 0387283137 |
Download Methods and Applications of Singular Perturbations Book in PDF, Epub and Kindle
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
| Author | : F. Brent Sato |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1975 |
| Genre | : Boundary value problems |
| ISBN | : |
Download A Singular Boundary Value Problem Book in PDF, Epub and Kindle
The differential equation w"' + ww" + x(l - (w') 2 ) = 0, where X >_ 0, is an important equation in boundary layer theory. Various techniques have been used to prove the existence of solutions on [0,°°) satisfying various boundary conditions. In particular, in the context of an intermediate value property for operators on partially ordered sets developed by Muldowney and Willett [8], Gamlen and Muldowney [4] demonstrated the existence of a solution satisfying w(0) = a, w'(0) = b,w'(°°) = 1, where 0
| Author | : A.V. Bitsadze |
| Publisher | : Elsevier |
| Total Pages | : 212 |
| Release | : 2012-12-02 |
| Genre | : Mathematics |
| ISBN | : 0323162266 |
Download Boundary Value Problems For Second Order Elliptic Equations Book in PDF, Epub and Kindle
Applied Mathematics and Mechanics, Volume 5: Boundary Value Problems: For Second Order Elliptic Equations is a revised and augmented version of a lecture course on non-Fredholm elliptic boundary value problems, delivered at the Novosibirsk State University in the academic year 1964-1965. This seven-chapter text is devoted to a study of the basic linear boundary value problems for linear second order partial differential equations, which satisfy the condition of uniform ellipticity. The opening chapter deals with the fundamental aspects of the linear equations theory in normed linear spaces. This topic is followed by discussions on solutions of elliptic equations and the formulation of Dirichlet problem for a second order elliptic equation. A chapter focuses on the solution equation for the directional derivative problem. Another chapter surveys the formulation of the Poincaré problem for second order elliptic systems in two independent variables. This chapter also examines the theory of one-dimensional singular integral equations that allow the investigation of highly important classes of boundary value problems. The final chapter looks into other classes of multidimensional singular integral equations and related boundary value problems.
| Author | : Albert E. Heins |
| Publisher | : |
| Total Pages | : 6 |
| Release | : 1968 |
| Genre | : |
| ISBN | : |
Download Singular Integral Equations with Special Reference to Boundary-value Problems Book in PDF, Epub and Kindle
Research was conducted in the theory of singular integral equations which arise in certain initial value and boundary value problems that come from elliptic and hyperbolic equations. In particular, those related to axially symmetric boundary value problems were studied. Results were obtained on a singular boundary value problem for the Euler Darboux equation, an integral equation in diffraction theory, diffraction by a disc and a boundary value problem associated with the Tricomi equation. (Author).
| Author | : Michail Borsuk |
| Publisher | : Elsevier |
| Total Pages | : 538 |
| Release | : 2006-01-12 |
| Genre | : Mathematics |
| ISBN | : 0080461735 |
Download Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains Book in PDF, Epub and Kindle
The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. Key features: * New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
