Qualitative Theory Of Parabolic Equations
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Qualitative Theory Of Parabolic Equations Part 1
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Author : T. I. Zelenyak
language : en
Publisher: Walter de Gruyter
Release Date : 2011-09-06
Qualitative Theory Of Parabolic Equations Part 1 written by T. I. Zelenyak and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-06 with Mathematics categories.
In the qualitative theory of ordinary differential equations, the Liapunov method plays a fundamental role. To use their analogs for the analysis of stability of solutions to parabolic, hyperparabolic, and other nonclassical equations and systems, time-invariant a priori estimates have to be devised for solutions. In this publication only parabolic problems are considered. Here lie, mainly, the problems which have been investigated most thoroughly --- the construction of Liapunov functionals which naturally generalize Liapunov functions for nonlinear parabolic equations of the second order with one spatial variable. The authors establish stabilizing solutions theorems, and the necessary and sufficient conditions of general and asymptotic stability of stationary solutions, including the so-called critical case. Attraction domains for stable solutions of mixed problems for these equations are described. Furthermore, estimates for the number of stationary solutions are obtained.
Qualitative Theory Of Parabolic Equations
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Author : T.I. Zelenyak
language : en
Publisher:
Release Date : 1997
Qualitative Theory Of Parabolic Equations written by T.I. Zelenyak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Differential equations, Parabolic categories.
Qualitative Theory Of Parabolic Equations Part 1
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Author : M. P. Vishnevskii
language : en
Publisher:
Release Date :
Qualitative Theory Of Parabolic Equations Part 1 written by M. P. Vishnevskii and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Nonlinear Parabolic Equations
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Author : Lucio Boccardo
language : en
Publisher: Longman Publishing Group
Release Date : 1987
Nonlinear Parabolic Equations written by Lucio Boccardo and has been published by Longman Publishing Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Differential equations, Nonlinear categories.
Qualitative And Quantitative Analysis Of Nonlinear Systems
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Author : Michael Z. Zgurovsky
language : en
Publisher: Springer
Release Date : 2017-07-11
Qualitative And Quantitative Analysis Of Nonlinear Systems written by Michael Z. Zgurovsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-11 with Technology & Engineering categories.
Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and their approximations; (c) uniform global behavior of solutions in time; and (d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for the investigation of dissipative dynamical systems with several applications including nonlinear parabolic equations of divergent form, nonlinear stochastic equations of parabolic type, unilateral problems, nonlinear PDEs on Riemannian manifolds with or without boundary, contact problems as well as particular examples is established. As such, the book is addressed to a wide circle of mathematical, mechanical and engineering readers.
Qualitative Theory Of Differential Equations
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Author : Viktor Vladimirovich Nemytskii
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Qualitative Theory Of Differential Equations written by Viktor Vladimirovich Nemytskii and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
Book 22 in the Princeton Mathematical Series. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Methods For Partial Differential Equations
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Author : Marcelo R. Ebert
language : en
Publisher: Birkhäuser
Release Date : 2018-02-23
Methods For Partial Differential Equations written by Marcelo R. Ebert and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.
Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations
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Author : Ding Tong-ren
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-08-13
Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations written by Ding Tong-ren and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems. Elementary knowledge is emphasized by the detailed discussions on the fundamental theorems of the Cauchy problem, fixed-point theorems (especially the twist theorems), the principal idea of dynamical systems, the nonlinear oscillation of Duffing's equation, and some special analyses of particular differential equations. It also contains the latest research by the author as an integral part of the book.
Qualitative Theory Of Volterra Difference Equations
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Author : Youssef N. Raffoul
language : en
Publisher: Springer
Release Date : 2018-09-12
Qualitative Theory Of Volterra Difference Equations written by Youssef N. Raffoul and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-12 with Mathematics categories.
This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. Applications to real-world problems and open-ended problems are included throughout. This book will be of use as a primary reference to researchers and graduate students who are interested in the study of boundedness of solutions, the stability of the zero solution, or in the existence of periodic solutions using Lyapunov functionals and the notion of fixed point theory.
A First Course In The Qualitative Theory Of Differential Equations
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Author : James Hetao Liu
language : en
Publisher:
Release Date : 2003
A First Course In The Qualitative Theory Of Differential Equations written by James Hetao Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Differential equations, Nonlinear categories.
This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research-including details that other books in the field tend to overlook. Chapters 1-7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8-12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.