A Stability Technique for Evolution Partial Differential Equations

Author: Victor A. Galaktionov
Publisher: Springer Science & Business Media
ISBN: 1461220505
Format: PDF
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* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

Nonlinear Elliptic and Parabolic Problems

Author: Michel Chipot
Publisher: Springer Science & Business Media
ISBN: 9783764372668
Format: PDF, ePub
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The book offers an overview of some of the most important developments in the field of nonlinear analysis, including bifurcation theory, dynamical properties of parabolic semiflows, fluid dynamics, and degenerate parabolic problems.

The Porous Medium Equation

Author: Juan Luis Vazquez
Publisher: Oxford University Press
ISBN: 9780198569039
Format: PDF
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Aimed at research students and academics in mathematics and engineering, as well as engineering specialists, this book provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation.

Smoothing and Decay Estimates for Nonlinear Diffusion Equations

Author: Juan Luis Vázquez
Publisher: Oxford University Press
ISBN: 0199202974
Format: PDF, ePub, Mobi
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This text is concerned with quantitative aspects of the theory of nonlinear diffusion equations, whichappear as mathematical models in different branches of Physics, Chemistry, Biology and Engineering.

Evolution PDEs with Nonstandard Growth Conditions

Author: Stanislav Antontsev
Publisher: Springer
ISBN: 9462391122
Format: PDF, Docs
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This monograph offers the reader a treatment of the theory of evolution PDEs with nonstandard growth conditions. This class includes parabolic and hyperbolic equations with variable or anisotropic nonlinear structure. We develop methods for the study of such equations and present a detailed account of recent results. An overview of other approaches to the study of PDEs of this kind is provided. The presentation is focused on the issues of existence and uniqueness of solutions in appropriate function spaces and on the study of the specific qualitative properties of solutions, such as localization in space and time, extinction in a finite time and blow-up, or nonexistence of global in time solutions. Special attention is paid to the study of the properties intrinsic to solutions of equations with nonstandard growth.

Recent Trends in Nonlinear Partial Differential Equations I

Author: James B. Serrin
Publisher: American Mathematical Soc.
ISBN: 082188736X
Format: PDF, Mobi
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This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought t

Hamiltonian Partial Differential Equations and Applications

Author: Philippe Guyenne
Publisher: Springer
ISBN: 149392950X
Format: PDF, ePub, Docs
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This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Understanding Nonlinear Dynamics

Author: Daniel Kaplan
Publisher: Springer Science & Business Media
ISBN: 1461208238
Format: PDF, ePub
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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.

Stability of Dynamical Systems

Author: Xiaoxin Liao
Publisher: Elsevier
ISBN: 9780080550619
Format: PDF, ePub, Mobi
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The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers