Author: P.L. Sachdev
Publisher:
ISBN: 9780387879383
Category : Differential equations, Nonlinear
Languages : en
Pages :
Book Description
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Author: P.L. Sachdev
Publisher:
ISBN: 9780387879383
Category : Differential equations, Nonlinear
Languages : en
Pages :
Book Description
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.
Publisher:
ISBN: 9780387879383
Category : Differential equations, Nonlinear
Languages : en
Pages :
Book Description
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.
Asymptotics for Dissipative Nonlinear Equations
Author: Nakao Hayashi
Publisher: Springer Science & Business Media
ISBN: 3540320598
Category : Mathematics
Languages : en
Pages : 570
Book Description
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the 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.
Publisher: Springer Science & Business Media
ISBN: 3540320598
Category : Mathematics
Languages : en
Pages : 570
Book Description
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the 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.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Author: P.L. Sachdev
Publisher: Springer Science & Business Media
ISBN: 0387878092
Category : Mathematics
Languages : en
Pages : 240
Book Description
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.
Publisher: Springer Science & Business Media
ISBN: 0387878092
Category : Mathematics
Languages : en
Pages : 240
Book Description
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.
Large-Time Behavior of Solutions of Linear Dispersive Equations
Author: Daniel B. Dix
Publisher: Springer
ISBN: 3540695451
Category : Mathematics
Languages : en
Pages : 217
Book Description
This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.
Publisher: Springer
ISBN: 3540695451
Category : Mathematics
Languages : en
Pages : 217
Book Description
This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.
Translations of Mathematical Monographs
Author:
Publisher:
ISBN: 9780821821091
Category : Differential equations, Nonlinear
Languages : en
Pages : 285
Book Description
Publisher:
ISBN: 9780821821091
Category : Differential equations, Nonlinear
Languages : en
Pages : 285
Book Description
Asymptotic Analysis and the Numerical Solution of Partial Differential Equations
Author: Hans G. Kaper
Publisher: CRC Press
ISBN: 1482277069
Category : Mathematics
Languages : en
Pages : 283
Book Description
Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Publisher: CRC Press
ISBN: 1482277069
Category : Mathematics
Languages : en
Pages : 283
Book Description
Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Entropy Methods for Diffusive Partial Differential Equations
Author: Ansgar Jüngel
Publisher: Springer
ISBN: 3319342193
Category : Mathematics
Languages : en
Pages : 146
Book Description
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
Publisher: Springer
ISBN: 3319342193
Category : Mathematics
Languages : en
Pages : 146
Book Description
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
Instability in Models Connected with Fluid Flows I
Author: Claude Bardos
Publisher: Springer Science & Business Media
ISBN: 038775217X
Category : Technology & Engineering
Languages : en
Pages : 394
Book Description
In this authoritative and comprehensive volume, Claude Bardos and Andrei Fursikov have drawn together an impressive array of international contributors to present important recent results and perspectives in this area. The main subjects that appear here relate largely to mathematical aspects of the theory but some novel schemes used in applied mathematics are also presented. Various topics from control theory, including Navier-Stokes equations, are covered.
Publisher: Springer Science & Business Media
ISBN: 038775217X
Category : Technology & Engineering
Languages : en
Pages : 394
Book Description
In this authoritative and comprehensive volume, Claude Bardos and Andrei Fursikov have drawn together an impressive array of international contributors to present important recent results and perspectives in this area. The main subjects that appear here relate largely to mathematical aspects of the theory but some novel schemes used in applied mathematics are also presented. Various topics from control theory, including Navier-Stokes equations, are covered.
On the Asymptotic Stability of Solutions of Nonlinear Partial Differential Equations of Parabolic Type, Part 1
Author: Rangaswamy Narasimhan
Publisher:
ISBN:
Category :
Languages : en
Pages : 72
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 72
Book Description
Nelinejnye Nelokal'nye Uravneniâ V Teorii Voln
Author: Pavel Ivanovich Naumkin
Publisher: American Mathematical Soc.
ISBN: 9780821887691
Category : Science
Languages : en
Pages : 312
Book Description
This book is the first to concentrate on the theory of nonlinear nonlocal equations. The authors solve a number of problems concerning the asymptotic behavior of solutions of nonlinear evolution equations, the blow-up of solutions, and the global in time existence of solutions. In addition, a new classification of nonlinear nonlocal equations is introduced. A large class of these equations is treated by a single method, the main features of which are apriori estimates in different integral norms and use of the Fourier transform. This book will interest specialists in partial differential equations, as well as physicists and engineers.
Publisher: American Mathematical Soc.
ISBN: 9780821887691
Category : Science
Languages : en
Pages : 312
Book Description
This book is the first to concentrate on the theory of nonlinear nonlocal equations. The authors solve a number of problems concerning the asymptotic behavior of solutions of nonlinear evolution equations, the blow-up of solutions, and the global in time existence of solutions. In addition, a new classification of nonlinear nonlocal equations is introduced. A large class of these equations is treated by a single method, the main features of which are apriori estimates in different integral norms and use of the Fourier transform. This book will interest specialists in partial differential equations, as well as physicists and engineers.