Implicit Partial Differential Equations

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Implicit Partial Differential Equations

Bernard Dacorogna,Paolo Marcellini
Implicit Partial Differential Equations Book PDF

Author : Bernard Dacorogna,Paolo Marcellini
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215622

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Implicit Partial Differential Equations by Bernard Dacorogna,Paolo Marcellini Pdf

Nonlinear partial differential equations has become one of the main tools of mod ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes. In recent years, several mathematicians have investigated nonlinear equations, particularly those of the second order, both linear and nonlinear and either in divergence or nondivergence form. Quasilinear and fully nonlinear differential equations are relevant classes of such equations and have been widely examined in the mathematical literature. In this work we present a new family of differential equations called "implicit partial differential equations", described in detail in the introduction (c.f. Chapter 1). It is a class of nonlinear equations that does not include the family of fully nonlinear elliptic pdes. We present a new functional analytic method based on the Baire category theorem for handling the existence of almost everywhere solutions of these implicit equations. The results have been obtained for the most part in recent years and have important applications to the calculus of variations, nonlin ear elasticity, problems of phase transitions and optimal design; some results have not been published elsewhere.

Implicit Fractional Differential and Integral Equations

Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson
Implicit Fractional Differential and Integral Equations Book PDF

Author : Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 359 pages
File Size : 40,7 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 9783110553819

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Implicit Fractional Differential and Integral Equations by Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson Pdf

This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. ContentsPreliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

Implicit Functions and Solution Mappings

Asen L. Dontchev,R. Tyrrell Rockafellar
Implicit Functions and Solution Mappings Book PDF

Author : Asen L. Dontchev,R. Tyrrell Rockafellar
Publisher : Springer
Page : 495 pages
File Size : 51,9 Mb
Release : 2014-06-18
Category : Mathematics
ISBN : 9781493910373

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Implicit Functions and Solution Mappings by Asen L. Dontchev,R. Tyrrell Rockafellar Pdf

The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.

Partial Differential Equations

Walter A. Strauss
Partial Differential Equations Book PDF

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 41,6 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

The Implicit Function Theorem

Steven G. Krantz,Harold R. Parks
The Implicit Function Theorem Book PDF

Author : Steven G. Krantz,Harold R. Parks
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 54,5 Mb
Release : 2012-11-26
Category : Mathematics
ISBN : 9781461200598

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The Implicit Function Theorem by Steven G. Krantz,Harold R. Parks Pdf

The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non- smooth functions, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash--Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve. "The Implicit Function Theorem" is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas.

Numerical Partial Differential Equations: Finite Difference Methods

J.W. Thomas
Numerical Partial Differential Equations Finite Difference Methods Book PDF

Author : J.W. Thomas
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 54,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781489972781

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Numerical Partial Differential Equations: Finite Difference Methods by J.W. Thomas Pdf

What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.

Analysis And Differential Equations (Second Edition)

Odile Pons
Analysis And Differential Equations Second Edition Book PDF

Author : Odile Pons
Publisher : World Scientific
Page : 305 pages
File Size : 44,8 Mb
Release : 2022-12-19
Category : Mathematics
ISBN : 9789811268588

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Analysis And Differential Equations (Second Edition) by Odile Pons Pdf

The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.

The Numerical Solution of Ordinary and Partial Differential Equations

Granville Sewell
The Numerical Solution of Ordinary and Partial Differential Equations Book PDF

Author : Granville Sewell
Publisher : Academic Press
Page : 284 pages
File Size : 52,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483259147

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The Numerical Solution of Ordinary and Partial Differential Equations by Granville Sewell Pdf

The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.

Ordinary and Partial Differential Equations for the Beginner

László Székelyhidi
Ordinary and Partial Differential Equations for the Beginner Book PDF

Author : László Székelyhidi
Publisher : World Scientific Publishing Company
Page : 256 pages
File Size : 43,5 Mb
Release : 2016-05-24
Category : Mathematics
ISBN : 9789814725019

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Ordinary and Partial Differential Equations for the Beginner by László Székelyhidi Pdf

This textbook is intended for college, undergraduate and graduate students, emphasizing mainly on ordinary differential equations. However, the theory of characteristics for first order partial differential equations and the classification of second order linear partial differential operators are also included. It contains the basic material starting from elementary solution methods for ordinary differential equations to advanced methods for first order partial differential equations. In addition to the theoretical background, solution methods are strongly emphasized. Each section is completed with problems and exercises, and the solutions are also provided. There are special sections devoted to more applied tools such as implicit equations, Laplace transform, Fourier method, etc. As a novelty, a method for finding exponential polynomial solutions is presented which is based on the author's work in spectral synthesis. The presentation is self-contained, provided the reader has general undergraduate knowledge.

Numerical Solution of Partial Differential Equations

Gordon D. Smith
Numerical Solution of Partial Differential Equations Book PDF

Author : Gordon D. Smith
Publisher : Oxford University Press
Page : 356 pages
File Size : 41,9 Mb
Release : 1985
Category : Computers
ISBN : 0198596502

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Numerical Solution of Partial Differential Equations by Gordon D. Smith Pdf

Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM

John A. Trangenstein
Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD ROM Book PDF

Author : John A. Trangenstein
Publisher : Cambridge University Press
Page : 657 pages
File Size : 46,5 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9780521877268

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Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM by John A. Trangenstein Pdf

For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).

Computational Partial Differential Equations

Hans Petter Langtangen
Computational Partial Differential Equations Book PDF

Author : Hans Petter Langtangen
Publisher : Springer Science & Business Media
Page : 704 pages
File Size : 55,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662011706

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Computational Partial Differential Equations by Hans Petter Langtangen Pdf

Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

Elliptic–Hyperbolic Partial Differential Equations

Thomas H. Otway
Elliptic Hyperbolic Partial Differential Equations Book PDF

Author : Thomas H. Otway
Publisher : Springer
Page : 128 pages
File Size : 49,5 Mb
Release : 2015-07-08
Category : Mathematics
ISBN : 9783319197616

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Elliptic–Hyperbolic Partial Differential Equations by Thomas H. Otway Pdf

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.

Singular Nonlinear Partial Differential Equations

Raymond Gérard,Hidetoshi Tahara
Singular Nonlinear Partial Differential Equations Book PDF

Author : Raymond Gérard,Hidetoshi Tahara
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783322802842

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Singular Nonlinear Partial Differential Equations by Raymond Gérard,Hidetoshi Tahara Pdf

The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations.

Nonlinear Partial Differential Equations in Engineering

W. F. Ames
Nonlinear Partial Differential Equations in Engineering Book PDF

Author : W. F. Ames
Publisher : Academic Press
Page : 528 pages
File Size : 45,5 Mb
Release : 1965-01-01
Category : Mathematics
ISBN : 9780080955247

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Nonlinear Partial Differential Equations in Engineering by W. F. Ames Pdf

Nonlinear Partial Differential Equations in Engineering