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Author: Valentin Nikolaevich Monakhov Publisher: American Mathematical Soc. ISBN: 9780821898079 Category : Mathematics Languages : en Pages : 540
Book Description
This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.
Author: Valentin Nikolaevich Monakhov Publisher: American Mathematical Soc. ISBN: 9780821898079 Category : Mathematics Languages : en Pages : 540
Book Description
This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.
Author: J. T. Wloka Publisher: Cambridge University Press ISBN: 0521430119 Category : Mathematics Languages : en Pages : 659
Book Description
The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. Because many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises. This book is ideal for use in graduate level courses on partial differential equations, elliptic systems, pseudo-differential operators, and matrix analysis.
Author: A.V. Bitsadze Publisher: Elsevier ISBN: 0323162266 Category : Mathematics Languages : en Pages : 212
Book Description
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: Guo Chun Wen Publisher: Chapman & Hall/CRC ISBN: Category : Mathematics Languages : en Pages : 432
Book Description
This monograph mainly deals with several boundary value problems for linear and nonlinear elliptic equations and systems by using function theoretic methods. The established theory is systematic, the considered equations and systems, boundary conditions and domains are rather general. Various methods are used. As an application, the existence of nonlinear quasiconformal mappings onto canonical domains is proved.
Author: V. G. Maz_i_a Publisher: American Mathematical Soc. ISBN: 0821849832 Category : Mathematics Languages : en Pages : 618
Book Description
This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.
Author: Alex Amenta Publisher: American Mathematical Soc. ISBN: 1470442507 Category : Mathematics Languages : en Pages : 162
Book Description
A co-publication of the AMS and Centre de Recherches Mathématiques In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces. The authors use the so-called “first order approach” which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.
Author: M. A. Lavrent’ev Publisher: Courier Dover Publications ISBN: 0486160289 Category : Mathematics Languages : en Pages : 164
Book Description
Famous monograph by a distinguished mathematician presents an innovative approach to classical boundary value problems. The treatment employs the basic scheme first suggested by Hilbert and developed by Tonnelli. 1963 edition.
Author: J. I. Díaz Publisher: ISBN: Category : Boundary value problems Languages : en Pages : 344
Book Description
In this Research Note the author brings together the body of known work and presents many recent results relating to nonlinear partial differential equations that give rise to a free boundary--usually the boundary of the set where the solution vanishes identically. The formation of such a boundary depends on an adequate balance between two of the terms of the equation that represent the particular characteristics of the phenomenon under consideration: diffusion, absorption, convection, evolution etc. These balances do not occur in the case of a linear equation or an arbitrary nonlinear equation. Their characterization is studied for several classes of nonlinear equations relating to applications such as chemical reactions, non-Newtonian fluids, flow through porous media and biological populations. In this first volume, the free boundary for nonlinear elliptic equations is discussed. A second volume dealing with parabolic and hyperbolic equations is in preparation.
Author: Valentin Nikolaevich Monakhov
Author: Valentin Nikolaevich Monakhov
Author: J. T. Wloka
Author: A.V. Bitsadze
Author: Guo Chun Wen
Author: H Begehr
Author: V. G. Maz_i_a
Author: Alex Amenta
Author: M. A. Lavrent’ev![Boundary Value Problems for Elliptic Systems of [linear] Partial Differential Equations PDF](https://books.google.com/books/content/images/frontcover/P1nNHwAACAAJ?fife=w80-h100)
Author: Charles A. Hayes
Author: J. I. Díaz