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Author: Nakao Hayashi
Publisher: Gulf Professional Publishing
ISBN: 9780444515698
Category : Mathematics
Languages : en
Pages : 350
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Book Description
This book is the first attempt to develop systematically a general theory of the initial-boundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a half-line or on a segment. We study traditionally important problems, such as local and global existence of solutions and their properties, in particular much attention is drawn to the asymptotic behavior of solutions for large time. Up to now the theory of nonlinear initial-boundary value problems with a general pseudodifferential operator has not been well developed due to its difficulty. There are many open natural questions. Firstly how many boundary data should we pose on the initial-boundary value problems for its correct solvability? As far as we know there are few results in the case of nonlinear nonlocal equations. The methods developed in this book are applicable to a wide class of dispersive and dissipative nonlinear equations, both local and nonlocal. · For the first time the definition of pseudodifferential operator on a half-line and a segment is done · A wide class of nonlinear nonlocal and local equations is considered · Developed theory is general and applicable to different equations · The book is written clearly, many examples are considered · Asymptotic formulas can be used for numerical computations by engineers and physicists · The authors are recognized experts in the nonlinear wave phenomena
Author: Nakao Hayashi
Publisher: Gulf Professional Publishing
ISBN: 9780444515698
Category : Mathematics
Languages : en
Pages : 350
Get Book Here
Book Description
This book is the first attempt to develop systematically a general theory of the initial-boundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a half-line or on a segment. We study traditionally important problems, such as local and global existence of solutions and their properties, in particular much attention is drawn to the asymptotic behavior of solutions for large time. Up to now the theory of nonlinear initial-boundary value problems with a general pseudodifferential operator has not been well developed due to its difficulty. There are many open natural questions. Firstly how many boundary data should we pose on the initial-boundary value problems for its correct solvability? As far as we know there are few results in the case of nonlinear nonlocal equations. The methods developed in this book are applicable to a wide class of dispersive and dissipative nonlinear equations, both local and nonlocal. · For the first time the definition of pseudodifferential operator on a half-line and a segment is done · A wide class of nonlinear nonlocal and local equations is considered · Developed theory is general and applicable to different equations · The book is written clearly, many examples are considered · Asymptotic formulas can be used for numerical computations by engineers and physicists · The authors are recognized experts in the nonlinear wave phenomena
Author: Nakao Hayashi
Publisher: Springer
ISBN: 3540320601
Category : Mathematics
Languages : en
Pages : 570
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Book Description
This is the first book in world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Author: Lars Hörmander
Publisher: Springer Science & Business Media
ISBN: 9783540629214
Category : Mathematics
Languages : en
Pages : 308
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Book Description
In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.
Author: A.A. Kilbas
Publisher: Elsevier
ISBN: 9780444518323
Category : Mathematics
Languages : en
Pages : 550
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Book Description
This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.
Author: Michael Oberguggenberger
Publisher: CRC Press
ISBN: 9780849306495
Category : Mathematics
Languages : en
Pages : 396
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Book Description
Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.
Author: Sergio Albeverio
Publisher: Birkhäuser
ISBN: 3034880731
Category : Mathematics
Languages : en
Pages : 444
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Book Description
This volume focuses on recent developments in non-linear and hyperbolic equations. It will be a most valuable resource for researchers in applied mathematics, the theory of wavelets, and in mathematical and theoretical physics. Nine up-to-date contributions have been written on invitation by experts in the respective fields. The book is the third volume of the subseries "Advances in Partial Differential Equations".
Author: Doina Cioranescu
Publisher: Elsevier
ISBN: 0080537677
Category : Mathematics
Languages : en
Pages : 665
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Book Description
This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.
Author:
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 620
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Book Description
Author: Nakao Hayashi
Publisher: Elsevier Science
ISBN: 9780444515698
Category : Mathematics
Languages : en
Pages : 340
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Book Description
This book is the first attempt to develop systematically a general theory of the initial-boundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a half-line or on a segment. We study traditionally important problems, such as local and global existence of solutions and their properties, in particular much attention is drawn to the asymptotic behavior of solutions for large time. Up to now the theory of nonlinear initial-boundary value problems with a general pseudodifferential operator has not been well developed due to its difficulty. There are many open natural questions. Firstly how many boundary data should we pose on the initial-boundary value problems for its correct solvability? As far as we know there are few results in the case of nonlinear nonlocal equations. The methods developed in this book are applicable to a wide class of dispersive and dissipative nonlinear equations, both local and nonlocal. · For the first time the definition of pseudodifferential operator on a half-line and a segment is done · A wide class of nonlinear nonlocal and local equations is considered · Developed theory is general and applicable to different equations · The book is written clearly, many examples are considered · Asymptotic formulas can be used for numerical computations by engineers and physicists · The authors are recognized experts in the nonlinear wave phenomena
Author: Vicentiu D. Radulescu
Publisher: Hindawi Publishing Corporation
ISBN: 9774540395
Category : Differential equations, Elliptic
Languages : en
Pages : 205
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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.
