Pseudo Monotone Operator Theory For Unsteady Problems With Variable Exponents

Author : Alex Kaltenbach
Publisher : Springer Nature
Page : 364 pages
File Size : 51,5 Mb
Release : 2023-09-12
Category : Mathematics
ISBN : 9783031296703

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Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents by Alex Kaltenbach Pdf

This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier–Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner–Lebesgue spaces is not applicable. As a substitute for Bochner–Lebesgue spaces, variable Bochner–Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier–Stokes equations under general assumptions. Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.

Author : Lars Diening
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 49,8 Mb
Release : 2011-03-31
Category : Mathematics
ISBN : 9783642183621

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Lebesgue and Sobolev Spaces with Variable Exponents by Lars Diening Pdf

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Author : Panagiotis D. Panagiotopoulos
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642516771

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Hemivariational Inequalities by Panagiotis D. Panagiotopoulos Pdf

The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.

Author : Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Dušan D. Repovš
Publisher : Springer
Page : 577 pages
File Size : 43,6 Mb
Release : 2019-02-26
Category : Mathematics
ISBN : 9783030034306

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Nonlinear Analysis - Theory and Methods by Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Dušan D. Repovš Pdf

This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.

Author : Jean Mawhin
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 49,5 Mb
Release : 2013-04-17
Category : Science
ISBN : 9781475720617

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Critical Point Theory and Hamiltonian Systems by Jean Mawhin Pdf

FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN

Author : Titus Petrila,Damian Trif
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 53,9 Mb
Release : 2006-06-14
Category : Mathematics
ISBN : 9780387238388

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Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics by Titus Petrila,Damian Trif Pdf

The present book – through the topics and the problems approach – aims at filling a gap, a real need in our literature concerning CFD (Computational Fluid Dynamics). Our presentation results from a large documentation and focuses on reviewing the present day most important numerical and computational methods in CFD. Many theoreticians and experts in the field have expressed their - terest in and need for such an enterprise. This was the motivation for carrying out our study and writing this book. It contains an important systematic collection of numerical working instruments in Fluid Dyn- ics. Our current approach to CFD started ten years ago when the Univ- sity of Paris XI suggested a collaboration in the field of spectral methods for fluid dynamics. Soon after – preeminently studying the numerical approaches to Navier–Stokes nonlinearities – we completed a number of research projects which we presented at the most important inter- tional conferences in the field, to gratifying appreciation. An important qualitative step in our work was provided by the dev- opment of a computational basis and by access to a number of expert softwares. This fact allowed us to generate effective working programs for most of the problems and examples presented in the book, an - pect which was not taken into account in most similar studies that have already appeared all over the world.

Author : Rainer Klages,Günter Radons,Igor M. Sokolov
Publisher : John Wiley & Sons
Page : 614 pages
File Size : 46,8 Mb
Release : 2008-09-02
Category : Science
ISBN : 3527407227

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Anomalous Transport by Rainer Klages,Günter Radons,Igor M. Sokolov Pdf

This multi-author reference work provides a unique introduction to the currently emerging, highly interdisciplinary field of those transport processes that cannot be described by using standard methods of statistical mechanics. It comprehensively summarizes topics ranging from mathematical foundations of anomalous dynamics to the most recent experiments in this field. In so doing, this monograph extracts and emphasizes common principles and methods from many different disciplines while providing up-to-date coverage of this new field of research, considering such diverse applications as plasma physics, glassy material, cell science, and socio-economic aspects. The book will be of interest to both theorists and experimentalists in nonlinear dynamics, statistical physics and stochastic processes. It also forms an ideal starting point for graduate students moving into this area. 18 chapters written by internationally recognized experts in this field provide in-depth introductions to fundamental aspects of anomalous transport.

Author : Vicentiu D. Radulescu,Dusan D. Repovs
Publisher : CRC Press
Page : 323 pages
File Size : 45,5 Mb
Release : 2015-06-24
Category : Mathematics
ISBN : 9781498703444

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Partial Differential Equations with Variable Exponents by Vicentiu D. Radulescu,Dusan D. Repovs Pdf

Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences. The analysis developed in the book is based on the notion of a generalized or weak solution. This approach leads not only to the fundamental results of existence and multiplicity of weak solutions but also to several qualitative properties, including spectral analysis, bifurcation, and asymptotic analysis. The book examines the equations from different points of view while using the calculus of variations as the unifying theme. Readers will see how all of these diverse topics are connected to other important parts of mathematics, including topology, differential geometry, mathematical physics, and potential theory.

Author : Leszek Gasinski,Nikolaos S. Papageorgiou
Publisher : CRC Press
Page : 992 pages
File Size : 43,6 Mb
Release : 2005-07-27
Category : Mathematics
ISBN : 1584884843

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Nonlinear Analysis by Leszek Gasinski,Nikolaos S. Papageorgiou Pdf

Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.

Author : Ravi P. Agarwal,Kanishka Perera
Publisher : Hindawi Publishing Corporation
Page : 1268 pages
File Size : 44,6 Mb
Release : 2006
Category : Difference equations
ISBN : 9775945380

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Proceedings of the Conference on Differential & Difference Equations and Applications by Ravi P. Agarwal,Kanishka Perera Pdf

Author : Svatopluk Fucik,Alois Kufner
Publisher : Elsevier
Page : 360 pages
File Size : 48,6 Mb
Release : 2014-12-03
Category : Technology & Engineering
ISBN : 9781483278377

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Nonlinear Differential Equations by Svatopluk Fucik,Alois Kufner Pdf

Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations.

Author : C.M. Dafermos,Milan Pokorny
Publisher : Elsevier
Page : 609 pages
File Size : 49,7 Mb
Release : 2008-10-06
Category : Mathematics
ISBN : 9780080931975

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Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Milan Pokorny Pdf

The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Author : Konrad Knopp
Publisher : Courier Corporation
Page : 212 pages
File Size : 55,6 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9780486152042

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Infinite Sequences and Series by Konrad Knopp Pdf

Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.

Author : Jan Chabrowski
Publisher : World Scientific
Page : 256 pages
File Size : 46,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9810240767

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Weak Convergence Methods for Semilinear Elliptic Equations by Jan Chabrowski Pdf

This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonlinear Schr”dinger equation which appears in mathematical modeling phenomena arising in nonlinear optics and plasma physics. Solutions to these problems are found as critical points of variational functionals. The main difficulty in examining the compactness of Palais-Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains. In this book we develop the concentration-compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences. This tool, combined with some basic methods from the Lusternik-Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions. The book also emphasizes the effect of the graph topology of coefficients on the existence of multiple solutions.

Author : Vicentiu D. Radulescu,Vicenţiu D. Rădulescu
Publisher : Hindawi Publishing Corporation
Page : 205 pages
File Size : 48,9 Mb
Release : 2008
Category : Differential equations, Elliptic
ISBN : 9789774540394

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Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations by Vicentiu D. Radulescu,Vicenţiu D. Rădulescu Pdf

This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.