Boundary-value Problems with Free Boundaries for Elliptic Systems of Equations

Boundary-value Problems with Free Boundaries for Elliptic Systems of Equations PDF

Author: Valentin Nikolaevich Monakhov

Publisher: American Mathematical Soc.

Published: 1983

Total Pages: 540

ISBN-13: 9780821898079

DOWNLOAD EBOOK →

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.

Boundary Value Problems for Elliptic Systems

Boundary Value Problems for Elliptic Systems PDF

Author: J. T. Wloka

Publisher: Cambridge University Press

Published: 1995-07-28

Total Pages: 659

ISBN-13: 0521430119

DOWNLOAD EBOOK →

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.

Boundary Value Problems For Second Order Elliptic Equations

Boundary Value Problems For Second Order Elliptic Equations PDF

Author: A.V. Bitsadze

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 212

ISBN-13: 0323162266

DOWNLOAD EBOOK →

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.

Boundary Value Problems for Elliptic Equations and Systems

Boundary Value Problems for Elliptic Equations and Systems PDF

Author: Guo Chun Wen

Publisher: Chapman & Hall/CRC

Published: 1990

Total Pages: 432

ISBN-13:

DOWNLOAD EBOOK →

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.

Elliptic Equations in Polyhedral Domains

Elliptic Equations in Polyhedral Domains PDF

Author: V. G. Maz_i_a

Publisher: American Mathematical Soc.

Published: 2010-04-22

Total Pages: 618

ISBN-13: 0821849832

DOWNLOAD EBOOK →

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.

Nonlinear Partial Differential Equations and Free Boundaries: Elliptic equations

Nonlinear Partial Differential Equations and Free Boundaries: Elliptic equations PDF

Author: J. I. Díaz

Publisher:

Published: 1985

Total Pages: 344

ISBN-13:

DOWNLOAD EBOOK →

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.

Boundary Value Problems for Partial Differential Equations and Applications in Electrodynamics

Boundary Value Problems for Partial Differential Equations and Applications in Electrodynamics PDF

Author: N. E. Tovmasyan

Publisher: World Scientific

Published: 1994

Total Pages: 252

ISBN-13: 9789810213510

DOWNLOAD EBOOK →

The book is devoted to boundary value problems for general partial differential equations. Efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of analytic functions and having great theoretical and practical importance are developed.A new approach to the investigation of electromagnetic fields is sketched, permitting laws of propagation of electromagnetic energy at a great distance, is outlined and asymptotic formulae for solutions of Maxwell's equation is obtained. These equations are also applied to the efficient resolution of problems.The book is based mostly on the investigation of the author, a considerable part of which being published for the first time.

Lanterna Rally - Theme by Grace Themes