Author : Shuichi Kawashima
Publisher : World Scientific
Page : 378 pages
File Size : 27,33 MB
Release : 1998
Category : Mathematics
ISBN : 9789810233969
In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Author : Pao-Liu Chow
Publisher : CRC Press
Page : 336 pages
File Size : 41,94 MB
Release : 2014-12-10
Category : Mathematics
ISBN : 1466579552
Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Lévy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of material. New to the Second Edition Two sections on the Lévy type of stochastic integrals and the related stochastic differential equations in finite dimensions Discussions of Poisson random fields and related stochastic integrals, the solution of a stochastic heat equation with Poisson noise, and mild solutions to linear and nonlinear parabolic equations with Poisson noises Two sections on linear and semilinear wave equations driven by the Poisson type of noises Treatment of the Poisson stochastic integral in a Hilbert space and mild solutions of stochastic evolutions with Poisson noises Revised proofs and new theorems, such as explosive solutions of stochastic reaction diffusion equations Additional applications of stochastic PDEs to population biology and finance Updated section on parabolic equations and related elliptic problems in Gauss–Sobolev spaces The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population growth model in a random environment, and a stochastic model in bond market theory. The author also explores the connection of stochastic PDEs to infinite-dimensional stochastic analysis.
Author : Tomás Roubicek
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 12,83 MB
Release : 2006-01-17
Category : Mathematics
ISBN : 3764373970
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.
Author : Simo Särkkä
Publisher : Cambridge University Press
Page : 327 pages
File Size : 11,47 MB
Release : 2019-05-02
Category : Business & Economics
ISBN : 1316510085
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author : A. Naess
Publisher : Springer Science & Business Media
Page : 527 pages
File Size : 40,91 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9400903219
The IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics, held in Trondheim July 3-7, 1995, was the eighth of a series of IUTAM sponsored symposia which focus on the application of stochastic methods in mechanics. The previous meetings took place in Coventry, UK (1972), Sout'hampton, UK (1976), FrankfurtjOder, Germany (1982), Stockholm, Sweden (1984), Innsbruckjlgls, Austria (1987), Turin, Italy (1991) and San Antonio, Texas (1993). The symposium provided an extraordinary opportunity for scholars to meet and discuss recent advances in stochastic mechanics. The participants represented a wide range of expertise, from pure theoreticians to people primarily oriented toward applications. A significant achievement of the symposium was the very extensive discussions taking place over the whole range from highly theoretical questions to practical engineering applications. Several presentations also clearly demonstrated the substantial progress that has been achieved in recent years in terms of developing and implement ing stochastic analysis techniques for mechanical engineering systems. This aspect was further underpinned by specially invited extended lectures on computational stochastic mechanics, engineering applications of stochastic mechanics, and nonlinear active control. The symposium also reflected the very active and high-quality research taking place in the field of stochastic stability. Ten presentations were given on this topic ofa total of47 papers. A main conclusion that can be drawn from the proceedings of this symposium is that stochastic mechanics as a subject has reached great depth and width in both methodology and applicability.
Author : S Kawashima
Publisher : World Scientific
Page : 366 pages
File Size : 10,67 MB
Release : 1998-06-17
Category : Mathematics
ISBN : 9814496367
In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Author : Michel Chipot
Publisher : CRC Press
Page : 254 pages
File Size : 42,67 MB
Release : 1993-11-01
Category : Mathematics
ISBN : 9780582227699
This volume presents papers from the conferences given at the University of Metz in 1992, and presents some recent advances in various important domains of partial differential equations and applied mathematics. A special attempt has been made to make this work accessible to young researchers and non-specialists.
Author : George Adomian
Publisher : Academic Press
Page : 304 pages
File Size : 42,50 MB
Release : 2014-05-09
Category : Science
ISBN : 1483259099
Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science. This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology, medicine. This text discusses operator equations and the decomposition method. This book also explains the limitations, restrictions and assumptions made in differential equations involving stochastic process coefficients (the stochastic operator case), which yield results very different from the needs of the actual physical problem. Real-world application of mathematics to actual physical problems, requires making a reasonable model that is both realistic and solvable. The decomposition approach or model is an approximation method to solve a wide range of problems. This book explains an inherent feature of real systems—known as nonlinear behavior—that occurs frequently in nuclear reactors, in physiological systems, or in cellular growth. This text also discusses stochastic operator equations with linear boundary conditions. This book is intended for students with a mathematics background, particularly senior undergraduate and graduate students of advanced mathematics, of the physical or engineering sciences.
Author : Marius Ghergu
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 26,42 MB
Release : 2011-10-21
Category : Mathematics
ISBN : 3642226647
The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.
Author : Shin'ichirō Ei
Publisher : Mathematical Society of Japan, Japan
Page : 546 pages
File Size : 26,7 MB
Release : 2015
Category : Mathematics
ISBN : 9784864970228
This volume contains more than fifty peer-reviewed survey and research papers presented at the 4th MSJ-SI International Conference on Nonlinear Dynamics in Partial Differential Equations, held at Kyushu University, Kyushu, Japan, September 12-21, 2011. Nonlinear partial differential equations describing nonlinear dynamics are indispensable objects in many fields, including technology and social science. This book covers recent mathematical theories and techniques to analyze such nonlinear partial differential equations.
