A Closer Look of Nonlinear Reaction-Diffusion Equations, L. Rajendran, R. Swaminathan

Автор: Francesco Calogero
Название: Zeros of Polynomials and Solvable Nonlinear Evolution Equations
ISBN: 1108428592 ISBN-13(EAN): 9781108428590
Издательство: Cambridge Academ
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Цена: 98200.00 T
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Описание: Exploring a novel breakthrough in the identification and investigation of solvable and integrable nonlinearly coupled evolution ordinary differential equations (ODEs) or partial differential equations (PDEs).

Автор: Jesus Ildefonso Diaz, David Gomez-Castro, Tatiana A. Shaposhnikova
Название: Nonlinear Reaction-Diffusion Processes for Nanocomposites: Anomalous Improved Homogenization
ISBN: 3110647273 ISBN-13(EAN): 9783110647273
Издательство: Walter de Gruyter
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Цена: 121430.00 T
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Описание: The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jurgen Appell, Wurzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Torun, Poland Vicentiu D. Radulescu, Krakow, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jurgen Appell . Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy–Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Автор: N.G Lloyd; M.G. Ni; L.A. Peletier; J. Serrin
Название: Nonlinear Diffusion Equations and Their Equilibrium States, 3
ISBN: 1461267412 ISBN-13(EAN): 9781461267416
Издательство: Springer
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Цена: 139750.00 T
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Описание: Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math- ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter- est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = cp(U) + f(u). Here denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x 0, T] in space-time. FUn- damental questions concern the existence, uniqueness and regularity of so- lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.

Автор: Brian H. Gilding; Robert Kersner
Название: Travelling Waves in Nonlinear Diffusion-Convection Reaction
ISBN: 3034896387 ISBN-13(EAN): 9783034896382
Издательство: Springer
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Цена: 93160.00 T
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Описание: This monograph has grown out of research we started in 1987, although the foun- dations were laid in the 1970`s when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion.

Автор: Ivan A. Lukovsky
Название: Nonlinear Dynamics: Mathematical Models for Rigid Bodies with a Liquid
ISBN: 3110555360 ISBN-13(EAN): 9783110555363
Издательство: Walter de Gruyter
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Цена: 25970.00 T
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Описание: This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid.

Автор: N.V. Krylov
Название: Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations
ISBN: 1470447401 ISBN-13(EAN): 9781470447403
Издательство: Mare Nostrum (Eurospan)
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Цена: 107850.00 T
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Описание: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov-Safonov and the Evans-Krylov theorems, are taken from old sources, and the main results were obtained in the last few years.Presentation of these results is based on a generalization of the Fefferman-Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called ``ersatz'' existence theorems, saying that one can slightly modify ``any'' equation and get a ``cut-off'' equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

Автор: Ed Bueler
Название: PETSc for Partial Differential Equations: Numerical Solutions in C and Python
ISBN: 1611976308 ISBN-13(EAN): 9781611976304
Издательство: Mare Nostrum (Eurospan)
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Цена: 81090.00 T
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Описание: The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers.Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Автор: Svetlin Georgiev, Inci M. Erhan
Название: Nonlinear Integral Equations on Time Scales
ISBN: 1536150215 ISBN-13(EAN): 9781536150216
Издательство: Nova Science
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Цена: 215410.00 T
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Описание: This book presents an introduction to the theory of nonlinear integral equations on time scales. Many population discrete models such as the logistic model, the Ricker model, the Beverton-Holt model, Leslie-Gower competition model and others can be investigated using nonlinear integral equations on the set of the natural numbers. This book contains different analytical and numerical methods for investigation of nonlinear integral equations on time scales. It is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. Students in mathematical and physical sciences willfind many sections of direct relevance. This book contains nine chapters, and each chapter consists of numerous examples and exercises.

Автор: Hermann Martin, Saravi Masoud
Название: Nonlinear Ordinary Differential Equations: Analytical Approximation and Numerical Methods
ISBN: 8132238451 ISBN-13(EAN): 9788132238454
Издательство: Springer
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Цена: 55890.00 T
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Описание: A Brief Review of Elementary Analytical Methods for Solving Nonlinear ODEs.- Analytical Approximation Methods.- Further Analytical Approximation Methods and Some Applications.- Nonlinear Two-Point Boundary Value Problems.- Numerical Treatment of Parameterized Two-Point Boundary Value Problems.

Автор: Marchuk, Guri I. , Agoshkov, Valeri I. , Shutyae
Название: Adjoint Equations and Perturbation Algorithms in Nonlinear Problems
ISBN: 0367448580 ISBN-13(EAN): 9780367448585
Издательство: Taylor&Francis
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Цена: 67360.00 T
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Описание: This book presents the theory of adjoint equations in nonlinear problems and their applications to perturbation algorithms for solution of nonlinear problems in mathematical physics. It formulates a series of principles of construction of adjoint operators in nonlinear problems.

Автор: Lakshmikantham, V. , Koksal, S.
Название: Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations
ISBN: 0367395401 ISBN-13(EAN): 9780367395407
Издательство: Taylor&Francis
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Цена: 65320.00 T
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Описание: A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic, and hyperbolic type. This volume describes that technique, which has played a valuable role in unifying a variety of nonlinear problems, particularly when combined with the quasilinearization method. The first part of this monograph describes the general methodology using the classic approach, while the second part develops the same basic ideas via the variational technique. The text provides a useful and timely reference for applied scientists, engineers and numerical analysts.

Автор: Wu-Ming Liu; Emmanuel Kengne
Название: Schr?dinger Equations in Nonlinear Systems
ISBN: 9811365806 ISBN-13(EAN): 9789811365805
Издательство: Springer
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Цена: 121110.00 T
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Описание: This book explores the diverse types of Schr?dinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schr?dinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schr?dinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.