On the Asymptotic Stability of Solutions of Nonlinear Partial Differential Equations of Parabolic Type, Part 1 PDF Download
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Author: Rangaswamy Narasimhan
Publisher:
ISBN:
Category :
Languages : en
Pages : 72
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Book Description
Author: Rangaswamy Narasimhan
Publisher:
ISBN:
Category :
Languages : en
Pages : 72
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Book Description
Author: B. Fiedler
Publisher: Gulf Professional Publishing
ISBN: 0080532845
Category : Science
Languages : en
Pages : 1099
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Book Description
This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.
Author: Mark McKibben
Publisher: CRC Press
ISBN: 1420092073
Category : Mathematics
Languages : en
Pages : 458
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Book Description
Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations provides an engaging, accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research. It gives nonspecialists, even those with minimal prior exposure to analysis, the foundation to understand what evolution equations are and how to work with them in various areas of practice. After presenting the essentials of analysis, the book discusses homogenous finite-dimensional ordinary differential equations. Subsequent chapters then focus on linear homogenous abstract, nonhomogenous linear, semi-linear, functional, Sobolev-type, neutral, delay, and nonlinear evolution equations. The final two chapters explore research topics, including nonlocal evolution equations. For each class of equations, the author develops a core of theoretical results concerning the existence and uniqueness of solutions under various growth and compactness assumptions, continuous dependence upon initial data and parameters, convergence results regarding the initial data, and elementary stability results. By taking an applications-oriented approach, this self-contained, conversational-style book motivates readers to fully grasp the mathematical details of studying evolution equations. It prepares newcomers to successfully navigate further research in the field.
Author: Lucio Boccardo
Publisher: Longman Publishing Group
ISBN:
Category : Mathematics
Languages : en
Pages : 252
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Book Description
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 568
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Book Description
Author: Jianhong Wu
Publisher: Springer Science & Business Media
ISBN: 1461240506
Category : Mathematics
Languages : en
Pages : 441
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Book Description
Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.
Author: John Rozier Cannon
Publisher: Cambridge University Press
ISBN: 9780521302432
Category : Mathematics
Languages : en
Pages : 522
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Book Description
This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.
Author: Tomáš Roubíček
Publisher: Springer Science & Business Media
ISBN: 3034805136
Category : Mathematics
Languages : en
Pages : 476
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Book Description
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook. The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and PhD students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems. ------ The monograph contains a wealth of material in both the abstract theory of steady-state or evolution equations of monotone and accretive type and concrete applications to nonlinear partial differential equations from mathematical modeling. The organization of the material is well done, and the presentation, although concise, is clear, elegant and rigorous. (...) this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists interested in the analysis of (...) nonlinear differential models of the real world. (Mathematical Reviews)
Author:
Publisher: DEStech Publications, Inc
ISBN: 1605951935
Category : Computers
Languages : en
Pages : 1356
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Book Description
The 6th International Conference on Computational and Information Sciences (ICCIS2014) will be held in NanChong, China. The 6th International Conference on Computational and Information Sciences (ICCIS2014)aims at bringing researchers in the areas of computational and information sciences to exchange new ideas and to explore new ground. The goal of the conference is to push the application of modern computing technologies to science, engineering, and information technologies.Following the success of ICCIS2004,ICCIS2010 and ICCIS2011,ICCIS2012,ICCIS2013,ICCIS2014 conference will consist of invited keynote presentations and contributed presentations of latest developments in computational and information sciences. The 2014 International Conference on Computational and Information Sciences (ICCIS 2014), now in its sixth run, has become one of the premier conferences in this dynamic and exciting field. The goal of ICCIS is to catalyze the communications among various communities in computational and information sciences. ICCIS provides a venue for the participants to share their recent research and development, to seek for collaboration resources and opportunities, and to build professional networks.
Author: Hal L. Smith
Publisher: American Mathematical Soc.
ISBN: 0821844873
Category : Mathematics
Languages : en
Pages : 186
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Book Description
This book presents comprehensive treatment of a rapidly developing area with many potential applications: the theory of monotone dynamical systems and the theory of competitive and cooperative differential equations. The primary aim is to provide potential users of the theory with techniques, results, and ideas useful in applications, while at the same time providing rigorous proofs. Among the topics discussed in the book are continuous-time monotone dynamical systems, and quasimonotone and nonquasimonotone delay differential equations. The book closes with a discussion of applications to quasimonotone systems of reaction-diffusion type. Throughout the book, applications of the theory to many mathematical models arising in biology are discussed. Requiring a background in dynamical systems at the level of a first graduate course, this book is useful to graduate students and researchers working in the theory of dynamical systems and its applications.
