Compactness Methods for Nonlinear Evolutions PDF Download
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Author: Ioan I. Vrabie
Publisher: Longman Scientific and Technical
ISBN:
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Author: Ioan I. Vrabie
Publisher: Longman Scientific and Technical
ISBN:
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Author: Ioan I Vrabie
Publisher: CRC Press
ISBN: 9780582248724
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This monograph provides a self-contained and comprehensive account of the most significant existence results obtained over the past two decades referring to some remarkable classes of ill-posed problems governed by non-accretive operators. All the results are derived from several compactness arguments, due mainly to the author, and are suitably illustrated by examples arising from various concrete problems - for example, nonlinear diffusion, heat conduction in materials with memory, fluid dynamics, and vibrations of a string with memory. Reference is made to optimal control theory in order to emphasize the degree of applicability of abstract compactness methods. Special attention is paid to multivalued perturbations of m-accretive operators; this case is analyzed under appropriate assumptions in order to allow the use of the general results in the study of some specific problems of great practical interest: reaction-diffusion and closed loop systems. Some biographical comments and open problems are also included. This new edition contains a number of improvements, corrections and insertions which both simplify and update the material. The book will be of interest to graduate students and specialists working in abstract evolution equations, partial differential equations, reaction-diffusion systems and ill-posed problems. A knowledge of topology, functional analysis and ordinary differential equations to undergraduate level is assumed.
Author: Songmu Zheng
Publisher: CRC Press
ISBN: 0203492226
Category : Mathematics
Languages : en
Pages : 304
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Book Description
Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator
Author: Nicolae H. Pavel
Publisher: Springer
ISBN: 3540471863
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.
Author: Delma Joseph Hebert
Publisher:
ISBN:
Category : Brownian motion processes
Languages : en
Pages : 124
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Book Description
Author: J. Kral
Publisher: Springer Science & Business Media
ISBN: 1461344255
Category : Mathematics
Languages : en
Pages : 138
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Book Description
Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.
Author: Monica-Dana Burlică
Publisher: CRC Press
ISBN: 1498746462
Category : Mathematics
Languages : en
Pages : 362
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Book Description
Filling a gap in the literature, Delay Differential Evolutions Subjected to Nonlocal Initial Conditions reveals important results on ordinary differential equations (ODEs) and partial differential equations (PDEs). It presents very recent results relating to the existence, boundedness, regularity, and asymptotic behavior of global solutions for differential equations and inclusions, with or without delay, subjected to nonlocal implicit initial conditions. After preliminaries on nonlinear evolution equations governed by dissipative operators, the book gives a thorough study of the existence, uniqueness, and asymptotic behavior of global bounded solutions for differential equations with delay and local initial conditions. It then focuses on two important nonlocal cases: autonomous and quasi-autonomous. The authors next discuss sufficient conditions for the existence of almost periodic solutions, describe evolution systems with delay and nonlocal initial conditions, examine delay evolution inclusions, and extend some results to the multivalued case of reaction-diffusion systems. The book concludes with results on viability for nonlocal evolution inclusions.
Author: Viorel Barbu
Publisher: Springer Science & Business Media
ISBN: 1441955429
Category : Mathematics
Languages : en
Pages : 283
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Book Description
This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.
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: Yong Zhou
Publisher: Academic Press
ISBN: 0128047755
Category : Mathematics
Languages : en
Pages : 294
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Book Description
Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development. This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena. The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians. Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear. Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces. Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists The book provides the necessary background material required to go further into the subject and explore the rich research literature
