Nonlinear Theory of Pseudodifferential Equations on a Half-line PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Nonlinear Theory of Pseudodifferential Equations on a Half-line PDF full book. Access full book title Nonlinear Theory of Pseudodifferential Equations on a Half-line by Nakao Hayashi. Download full books in PDF and EPUB format.
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: 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
Get Book Here
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: A.A. Kilbas
Publisher: Elsevier
ISBN: 9780444518323
Category : Mathematics
Languages : en
Pages : 550
Get Book Here
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:
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 620
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 916
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 442
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 544
Get Book Here
Book Description
Author: Grard Iooss
Publisher: American Mathematical Soc.
ISBN: 0821843826
Category : Science
Languages : en
Pages : 144
Get Book Here
Book Description
The authors consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity $g$ and resulting from the nonlinear interaction of two simply periodic travelling waves making an angle $2\theta$ between them. Denoting by $\mu =gL/c^{2}$ the dimensionless bifurcation parameter ( $L$ is the wave length along the direction of the travelling wave and $c$ is the velocity of the wave), bifurcation occurs for $\mu = \cos \theta$. For non-resonant cases, we first give a large family of formal three-dimensional gravity travelling waves, in the form of an expansion in powers of the amplitudes of two basic travelling waves. ``Diamond waves'' are a particular case of such waves, when they are symmetric with respect to the direction of propagation. The main object of the paper is the proof of existence of such symmetric waves having the above mentioned asymptotic expansion. Due to the occurence of small divisors, the main difficulty is the inversion of the linearized operator at a non trivial point, for applying the Nash Moser theorem. This operator is the sum of a second order differentiation along a certain direction, and an integro-differential operator of first order, both depending periodically of coordinates. It is shown that for almost all angles $\theta$, the 3-dimensional travelling waves bifurcate for a set of ``good'' values of the bifurcation parameter having asymptotically a full measure near the bifurcation curve in the parameter plane $(\theta,\mu ).$
Author: A. Dold
Publisher: Springer
ISBN: 1489945814
Category : Mathematics
Languages : en
Pages : 82
Get Book Here
Book Description
Author: A. S. Markus
Publisher: American Mathematical Soc.
ISBN: 0821890824
Category : Education
Languages : en
Pages : 256
Get Book Here
Book Description
This monograph contains an exposition of the foundations of the spectral theory of polynomial operator pencils acting in a Hilbert space. Spectral problems for polynomial pencils have attracted a steady interest in the last 35 years, mainly because they arise naturally in such diverse areas of mathematical physics as differential equations and boundary value problems, controllable systems, the theory of oscillations and waves, elasticity theory, and hydromechanics. In this book, the author devotes most of his attention to the fundamental results of Keldysh on multiple completeness of the eigenvectors and associate vectors of a pencil, and on the asymptotic behavior of its eigenvalues and generalizations of these results. The author also presents various theorems on spectral factorization of pencils which grew out of known results of M. G. Krein and Heinz Langer. A large portion of the book involves the theory of selfadjoint pencils, an area having numerous applications. Intended for mathematicians, researchers in mechanics, and theoretical physicists interested in spectral theory and its applications, the book assumes a familiarity with the fundamentals of spectral theory of operators acting in a Hilbert space.
