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Author : Reiner Lauterbach
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (256 download)
Download or read book Symmetry Breaking at Non-positive Solutions of Semilinear Elliptic Equations written by Reiner Lauterbach and published by . This book was released on 1992 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814374342
Total Pages : 254 pages
Book Rating : 4.8/5 (143 download)
Download or read book Global Solution Curves for Semilinear Elliptic Equations written by Philip Korman and published by World Scientific. This book was released on 2012 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results.
Author : Takashi Suzuki
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110556286
Total Pages : 490 pages
Book Rating : 4.1/5 (15 download)
Download or read book Semilinear Elliptic Equations written by Takashi Suzuki and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-12 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.
Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814374350
Total Pages : 254 pages
Book Rating : 4.8/5 (143 download)
Download or read book Global Solution Curves for Semilinear Elliptic Equations written by Philip Korman and published by World Scientific. This book was released on 2012 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results.
Author : W.-M. Ni
Publisher : Springer Science & Business Media
ISBN 13 : 1461396085
Total Pages : 364 pages
Book Rating : 4.4/5 (613 download)
Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.
Author : Lucio Damascelli
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110537435
Total Pages : 346 pages
Book Rating : 4.1/5 (15 download)
Download or read book Morse Index of Solutions of Nonlinear Elliptic Equations written by Lucio Damascelli and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents in a unified manner the use of the Morse index, and especially its connections to the maximum principle, in the study of nonlinear elliptic equations. The knowledge or a bound on the Morse index of a solution is a very important qualitative information which can be used in several ways for different problems, in order to derive uniqueness, existence or nonexistence, symmetry, and other properties of solutions.
Author : Jerome Goldstein
Publisher : Elsevier
ISBN 13 : 1483271986
Total Pages : 332 pages
Book Rating : 4.4/5 (832 download)
Download or read book Mathematics Applied to Science written by Jerome Goldstein and published by Elsevier. This book was released on 2014-05-10 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Applied to Science: In Memoriam Edward D. Conway presents a compilation of articles as a lasting tribute to Edward Conway III. This book covers a variety of topics, including molecular electronic energies, partial differential equations, density matrix, electron density functional, and climate change. Organized into 13 chapters, this book begins with an overview of the large-time behavior of one-dimensional motion in a model gas whose particles have a discrete set of allowed velocities. This text then explores the operator splitting techniques for the solution of time dependent differential equations. Other chapters describe a Monte Carlo simulation procedure for evaluating the relaxation rate of an excited state vibrational population of a diatomic in a simple solvent. This book discusses as well the numerical solution of nonlinear differential equations. The final chapter deals with the physical, thermal, and dynamical properties near the surface of the Earth. This book is a valuable resource for mathematicians.
Author : Vitaly Volpert
Publisher : Springer Science & Business Media
ISBN 13 : 3034605374
Total Pages : 649 pages
Book Rating : 4.0/5 (346 download)
Download or read book Elliptic Partial Differential Equations written by Vitaly Volpert and published by Springer Science & Business Media. This book was released on 2011-03-03 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments . The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.
Author : Felix E. Browder
Publisher : American Mathematical Soc.
ISBN 13 : 0821814710
Total Pages : 556 pages
Book Rating : 4.8/5 (218 download)
Download or read book Nonlinear Functional Analysis and Its Applications, Part 1 written by Felix E. Browder and published by American Mathematical Soc.. This book was released on 1986 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 1084 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1084 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pascal Chossat
Publisher : World Scientific Publishing Company
ISBN 13 : 9813105445
Total Pages : 422 pages
Book Rating : 4.8/5 (131 download)
Download or read book Methods In Equivariant Bifurcations And Dynamical Systems written by Pascal Chossat and published by World Scientific Publishing Company. This book was released on 2000-02-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book.The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.
Author : Changpin Li
Publisher : World Scientific
ISBN 13 : 9814436461
Total Pages : 414 pages
Book Rating : 4.8/5 (144 download)
Download or read book Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis written by Changpin Li and published by World Scientific. This book was released on 2013 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation.Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed.In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc.In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications.
Author : Nassif Ghoussoub
Publisher : American Mathematical Soc.
ISBN 13 : 0821891529
Total Pages : 331 pages
Book Rating : 4.8/5 (218 download)
Download or read book Functional Inequalities: New Perspectives and New Applications written by Nassif Ghoussoub and published by American Mathematical Soc.. This book was released on 2013-04-09 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.
Author : Roderick Melnik
Publisher : Springer
ISBN 13 : 1493969692
Total Pages : 437 pages
Book Rating : 4.4/5 (939 download)
Download or read book Recent Progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science written by Roderick Melnik and published by Springer. This book was released on 2017-09-05 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science. The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.
Author : Peng Feng
Publisher :
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.3/5 (129 download)
Download or read book Pattern Formation in Some Nonlinear Systems written by Peng Feng and published by . This book was released on 2005 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yihong Du
Publisher : World Scientific
ISBN 13 : 9812834745
Total Pages : 373 pages
Book Rating : 4.8/5 (128 download)
Download or read book Recent Progress on Reaction-diffusion Systems and Viscosity Solutions written by Yihong Du and published by World Scientific. This book was released on 2009 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of survey and research articles expanding on the theme of the OC International Conference on Reaction-Diffusion Systems and Viscosity SolutionsOCO, held at Providence University, Taiwan, during January 3OCo6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Japan), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (USA), Kunimochi Sakamoto (Japan), Richard Tsai (USA), Mingxin Wang (China), Yoshio Yamada (Japan), Eiji Yanagida (Japan), and Xiao-Qiang Zhao (Canada).
Author : B. Fiedler
Publisher : Gulf Professional Publishing
ISBN 13 : 0080532845
Total Pages : 1099 pages
Book Rating : 4.0/5 (85 download)
Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
