Advances in Nonlinear Partial Differential Equations and Stochastics

Advances in Nonlinear Partial Differential Equations and Stochastics
Title Advances in Nonlinear Partial Differential Equations and Stochastics PDF eBook
Author Shuichi Kawashima
Publisher World Scientific
Pages 378
Release 1998
Genre Mathematics
ISBN 9789810233969

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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.

Stochastic Partial Differential Equations, Second Edition

Stochastic Partial Differential Equations, Second Edition
Title Stochastic Partial Differential Equations, Second Edition PDF eBook
Author Pao-Liu Chow
Publisher CRC Press
Pages 336
Release 2014-12-10
Genre Mathematics
ISBN 1466579552

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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.

Applied Stochastic Differential Equations

Applied Stochastic Differential Equations
Title Applied Stochastic Differential Equations PDF eBook
Author Simo Särkkä
Publisher Cambridge University Press
Pages 327
Release 2019-05-02
Genre Business & Economics
ISBN 1316510085

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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Nonlinear Partial Differential Equations with Applications

Nonlinear Partial Differential Equations with Applications
Title Nonlinear Partial Differential Equations with Applications PDF eBook
Author Tomás Roubicek
Publisher Springer Science & Business Media
Pages 415
Release 2006-01-17
Genre Mathematics
ISBN 3764373970

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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.

IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics

IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics
Title IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics PDF eBook
Author A. Naess
Publisher Springer Science & Business Media
Pages 527
Release 2012-12-06
Genre Technology & Engineering
ISBN 9400903219

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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.

Advances In Nonlinear Partial Differential Equations And Stochastics

Advances In Nonlinear Partial Differential Equations And Stochastics
Title Advances In Nonlinear Partial Differential Equations And Stochastics PDF eBook
Author S Kawashima
Publisher World Scientific
Pages 366
Release 1998-06-17
Genre Mathematics
ISBN 9814496367

Download Advances In Nonlinear Partial Differential Equations And Stochastics Book in PDF, Epub and Kindle

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.

Advanced Synergetics

Advanced Synergetics
Title Advanced Synergetics PDF eBook
Author Hermann Haken
Publisher Springer Science & Business Media
Pages 371
Release 2012-12-06
Genre Science
ISBN 3642455530

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This text on the interdisciplinary field of synergetics will be of interest to students and scientists in physics, chemistry, mathematics, biology, electrical, civil and mechanical engineering, and other fields. It continues the outline of basic con cepts and methods presented in my book Synergetics. An Introduction, which has by now appeared in English, Russian, J apanese, Chinese, and German. I have written the present book in such a way that most of it can be read in dependently of my previous book, though occasionally some knowledge of that book might be useful. But why do these books address such a wide audience? Why are instabilities such a common feature, and what do devices and self-organizing systems have in common? Self-organizing systems acquire their structures or functions without specific interference from outside. The differentiation of cells in biology, and the process of evolution are both examples of self-organization. Devices such as the electronic oscillators used in radio transmitters, on the other hand, are man made. But we often forget that in many cases devices function by means of pro cesses which are also based on self-organization. In an electronic oscillator the motion of electrons becomes coherent without any coherent driving force from the outside; the device is constructed in such a way as to permit specific collective motions of the electrons. Quite evidently the dividing line between self-organiz ing systems and man-made devices is not at all rigid.