Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations PDF Download

Author: Victor A. Galaktionov
Publisher: CRC Press
ISBN: 1482251736
Category : Mathematics
Languages : en
Pages : 569

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Book Description
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs. The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking common features. The book describes many properties of the equations and examines traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities. Preparing readers for more advanced mathematical PDE analysis, the book demonstrates that quasilinear degenerate higher-order PDEs, even exotic and awkward ones, are not as daunting as they first appear. It also illustrates the deep features shared by several types of nonlinear PDEs and encourages readers to develop further this unifying PDE approach from other viewpoints.

Author: Victor A. Sadovnichiy
Publisher: Springer Nature
ISBN: 303050302X
Category : Mathematics
Languages : en
Pages : 525

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Book Description
This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields

Author: Kiyoshi Mochizuki
Publisher: CRC Press
ISBN: 1498756034
Category : Mathematics
Languages : en
Pages : 232

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Book Description
The book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the first half of this book, the classical results of spectral and scattering theory: the selfadjointness, essential spectrum, absolute continuity of the continuous spectrum, spectral representations, short-range and long-range scattering are summarized. In the second half, recent results: scattering of Schrodinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and some applications are discussed.

Author: Prof. Dr. Pavol Quittner
Publisher: Springer
ISBN: 3030182223
Category : Mathematics
Languages : en
Pages : 719

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Book Description
This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.

Author: Ronald E. Mickens
Publisher: CRC Press
ISBN: 1482230798
Category : Mathematics
Languages : en
Pages : 551

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Book Description
Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced to

Author: Vicentiu D. Radulescu
Publisher: CRC Press
ISBN: 1498703445
Category : Mathematics
Languages : en
Pages : 323

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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.

Author: Luca Lorenzi
Publisher: CRC Press
ISBN: 1315355620
Category : Mathematics
Languages : en
Pages : 572

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Book Description
The second edition of this book has a new title that more accurately reflects the table of contents. Over the past few years, many new results have been proven in the field of partial differential equations. This edition takes those new results into account, in particular the study of nonautonomous operators with unbounded coefficients, which has received great attention. Additionally, this edition is the first to use a unified approach to contain the new results in a singular place.

Author: Roman Cherniha
Publisher: CRC Press
ISBN: 1351650874
Category : Mathematics
Languages : en
Pages : 244

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Book Description
It is well known that symmetry-based methods are very powerful tools for investigating nonlinear partial differential equations (PDEs), notably for their reduction to those of lower dimensionality (e.g. to ODEs) and constructing exact solutions. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated problems. The book summarises the results derived by the authors during the last 10 years and those obtained by some other authors.

Author: Charles L. Byrne
Publisher: CRC Press
ISBN: 1482241854
Category : Computers
Languages : en
Pages : 436

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Book Description
Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics-including familiarity with Fourier series, matrices, probab

Author: John Harding
Publisher: CRC Press
ISBN: 1498735290
Category : Mathematics
Languages : en
Pages : 251

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Book Description
Type-2 fuzzy sets extend both ordinary and interval-valued fuzzy sets to allow distributions, rather than single values, as degrees of membership. Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets. The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval explo