**Author**: Vicentiu D. Radulescu

**Publisher:**Hindawi Publishing Corporation

**ISBN:**9774540395

**Size**: 49.62 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**208

**View:**945

**Book Description:**This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.

## Linear And Semilinear Partial Differential Equations

**Author**: Radu Precup

**Publisher:**Walter de Gruyter

**ISBN:**3110269058

**Size**: 24.21 MB

**Format:**PDF, ePub, Mobi

**Category :**Mathematics

**Languages :**en

**Pages :**296

**View:**1384

**Book Description:**This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions. The solution operators associated to non-homogeneous equations are used to make transition to the theory of nonlinear PDEs. Organized on three parts, this material is suitable for three one-semester courses, a beginning one in the frame of classical analysis, a more advanced course in modern theory and a master course in semi-linear equations.

## Numerical Analysis Of Partial Differential Equations

**Author**: S. H. Lui

**Publisher:**John Wiley & Sons

**ISBN:**0470647280

**Size**: 38.30 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**512

**View:**3259

**Book Description:**A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

## Partial Differential Equations With Variable Exponents

**Author**: Vicentiu D. Radulescu

**Publisher:**CRC Press

**ISBN:**1498703445

**Size**: 51.62 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**323

**View:**6001

**Book Description:**Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences. The analysis developed in the book is based on the notion of a generalized or weak solution. This approach leads not only to the fundamental results of existence and multiplicity of weak solutions but also to several qualitative properties, including spectral analysis, bifurcation, and asymptotic analysis. The book examines the equations from different points of view while using the calculus of variations as the unifying theme. Readers will see how all of these diverse topics are connected to other important parts of mathematics, including topology, differential geometry, mathematical physics, and potential theory.

## Bulletin Of The American Mathematical Society

**Author**: American Mathematical Society

**Publisher:**

**ISBN:**

**Size**: 20.56 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**

**View:**2080

**Book Description:**

## Mathematical Reviews

**Author**:

**Publisher:**

**ISBN:**

**Size**: 43.19 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**

**View:**6942

**Book Description:**

## Partial Differential Equations I

**Author**: Michael Eugene Taylor

**Publisher:**Springer Science & Business Media

**ISBN:**9780387946535

**Size**: 67.95 MB

**Format:**PDF, ePub, Mobi

**Category :**Mathematics

**Languages :**en

**Pages :**563

**View:**1759

**Book Description:**This book is intended to be a comprehensive introduction to the subject of partial differential equations. It should be useful to graduate students at all levels beyond that of a basic course in measure theory. It should also be of interest to professional mathematicians in analysis, mathematical physics, and differential geometry. This work will be divided into three volumes, the first of which focuses on the theory of ordinary differential equations and a survey of basic linear PDEs.

## Qualitative Methods In Nonlinear Mechanics

**Author**: John Tinsley Oden

**Publisher:**Prentice Hall

**ISBN:**

**Size**: 43.54 MB

**Format:**PDF, ePub, Docs

**Category :**Science

**Languages :**en

**Pages :**271

**View:**3553

**Book Description:**

## Nonlinear Analysis And Semilinear Elliptic Problems

**Author**: Antonio Ambrosetti

**Publisher:**Cambridge University Press

**ISBN:**9780521863209

**Size**: 40.17 MB

**Format:**PDF, Mobi

**Category :**Mathematics

**Languages :**en

**Pages :**316

**View:**7696

**Book Description:**A graduate text explaining how methods of nonlinear analysis can be used to tackle nonlinear differential equations. Suitable for mathematicians, physicists and engineers, topics covered range from elementary tools of bifurcation theory and analysis to critical point theory and elliptic partial differential equations. The book is amply illustrated with many exercises.

## Qualitative Theory Of Dynamical Systems

**Author**: Anthony N. Michel

**Publisher:**

**ISBN:**

**Size**: 34.25 MB

**Format:**PDF, Docs

**Category :**Differentiable dynamical systems

**Languages :**en

**Pages :**450

**View:**6309

**Book Description:**Written by renowned authorities in the field, Qualitative Theory of Dynamical Systems is an incomparable reference for pure and applied mathematicians; electrical and electronics, mechanical, civil, aerospace, and industrial engineers; control theorists; physicists; computer scientists; chemists; biologists; econometricians; and operations researchers; and the text of choice for all upper-level undergraduate and graduate students with a background in linear algebra, real analysis, and differential equations taking courses in stability theory, nonlinear systems, dynamical systems, or control systems.