Strongly Coupled Parabolic And Elliptic Systems

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Strongly Coupled Parabolic and Elliptic Systems

Author : Dung Le
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110608766
Total Pages : 198 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Strongly Coupled Parabolic and Elliptic Systems by : Dung Le

Download or read book Strongly Coupled Parabolic and Elliptic Systems written by Dung Le and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included. Contents Interpolation Gagliardo–Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(μ)–H1(μ)| Some algebraic inequalities Partial regularity

Strongly Coupled Elliptic Systems

Author : Linh Viet Nguyen
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.:/5 (759 download)

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Book Synopsis Strongly Coupled Elliptic Systems by : Linh Viet Nguyen

Download or read book Strongly Coupled Elliptic Systems written by Linh Viet Nguyen and published by . This book was released on 2006 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Regularity and Asymptotics for Strongly Nonlinear Parabolic Partial Differential Equations

Author : Maxim Trokhimtchouk
Publisher :
ISBN 13 :
Total Pages : 186 pages
Book Rating : 4.:/5 (35 download)

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Book Synopsis Regularity and Asymptotics for Strongly Nonlinear Parabolic Partial Differential Equations by : Maxim Trokhimtchouk

Download or read book Regularity and Asymptotics for Strongly Nonlinear Parabolic Partial Differential Equations written by Maxim Trokhimtchouk and published by . This book was released on 2009 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Cross Diffusion Systems

Author : Dung Le
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110795132
Total Pages : 236 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Cross Diffusion Systems by : Dung Le

Download or read book Cross Diffusion Systems written by Dung Le and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-10-24 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.

Handbook of Differential Equations: Stationary Partial Differential Equations

Author : Michel Chipot
Publisher : Elsevier
ISBN 13 : 0080560598
Total Pages : 618 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Differential Equations: Stationary Partial Differential Equations by : Michel Chipot

Download or read book Handbook of Differential Equations: Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2011-08-11 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems. * Collection of self-contained, state-of-the-art surveys * Written by well-known experts in the field * Informs and updates on all the latest developments

Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems

Author : Gershon Kresin
Publisher : American Mathematical Soc.
ISBN 13 : 0821889818
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems by : Gershon Kresin

Download or read book Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems written by Gershon Kresin and published by American Mathematical Soc.. This book was released on 2012-08-15 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.

Introduction to Reaction-Diffusion Equations

Author : King-Yeung Lam
Publisher : Springer Nature
ISBN 13 : 3031204220
Total Pages : 316 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Introduction to Reaction-Diffusion Equations by : King-Yeung Lam

Download or read book Introduction to Reaction-Diffusion Equations written by King-Yeung Lam and published by Springer Nature. This book was released on 2022-12-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.

Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

Author : Thomas Runst
Publisher :
ISBN 13 : 9783111766201
Total Pages : 547 pages
Book Rating : 4.7/5 (662 download)

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Book Synopsis Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations by : Thomas Runst

Download or read book Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations written by Thomas Runst and published by . This book was released on 1996 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Jürgen Appell, Würzburg, 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, Toruń, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Eduardo V. Teixeira, Free Boundary Problems: A Primer (2018) Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Dung Le, Strongly Coupled Parabolic and Elliptic Systems: Existence and Regularity of Strong and Weak Solutions (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)

Complex Analysis and Dynamical Systems VI

Author : Matania Ben-Artzi
Publisher : American Mathematical Soc.
ISBN 13 : 1470416530
Total Pages : 352 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Complex Analysis and Dynamical Systems VI by : Matania Ben-Artzi

Download or read book Complex Analysis and Dynamical Systems VI written by Matania Ben-Artzi and published by American Mathematical Soc.. This book was released on 2015-12-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19-24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers in this volume range over a wide variety of topics in Partial Differential Equations, Differential Geometry, and the Radon Transform. Taken together, the articles collected here provide the reader with a panorama of activity in partial differential equations and general relativity, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 667) is devoted to complex analysis, quasiconformal mappings, and complex dynamics. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).

Mathematical Neuroscience

Author : Stanislaw Brzychczy
Publisher : Academic Press
ISBN 13 : 0124104827
Total Pages : 201 pages
Book Rating : 4.1/5 (241 download)

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Book Synopsis Mathematical Neuroscience by : Stanislaw Brzychczy

Download or read book Mathematical Neuroscience written by Stanislaw Brzychczy and published by Academic Press. This book was released on 2013-08-16 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling

Reaction Diffusion Systems

Author : Gabriela Caristi
Publisher : CRC Press
ISBN 13 : 1000117197
Total Pages : 428 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Reaction Diffusion Systems by : Gabriela Caristi

Download or read book Reaction Diffusion Systems written by Gabriela Caristi and published by CRC Press. This book was released on 2020-10-07 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."

Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences

Author : Giovanni Naldi
Publisher : Springer Science & Business Media
ISBN 13 : 0817649468
Total Pages : 437 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences by : Giovanni Naldi

Download or read book Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences written by Giovanni Naldi and published by Springer Science & Business Media. This book was released on 2010-08-12 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.

Superlinear Parabolic Problems

Author : Prof. Dr. Pavol Quittner
Publisher : Springer
ISBN 13 : 3030182223
Total Pages : 719 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Superlinear Parabolic Problems by : Prof. Dr. Pavol Quittner

Download or read book Superlinear Parabolic Problems written by Prof. Dr. Pavol Quittner and published by Springer. This book was released on 2019-06-13 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.

Inequalities

Author : Everitt
Publisher : CRC Press
ISBN 13 : 9780824784881
Total Pages : 306 pages
Book Rating : 4.7/5 (848 download)

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Book Synopsis Inequalities by : Everitt

Download or read book Inequalities written by Everitt and published by CRC Press. This book was released on 1990-11-30 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of an international conference organized by the London Mathematical Society, held July 1987 at the U. of Birmingham, and dominated by the ghosts of Hardy, Littlewood and Polya, whose Inequalities (still the primary reference in the field) appeared in 1934. Thirteen essays summarize subse

Compactness Results for Time-dependent Parabolic Systems

Author : Reinhard Redlinger
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Compactness Results for Time-dependent Parabolic Systems by : Reinhard Redlinger

Download or read book Compactness Results for Time-dependent Parabolic Systems written by Reinhard Redlinger and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bifurcation and Symmetry

Author : BÖHMER
Publisher : Birkhäuser
ISBN 13 : 3034875363
Total Pages : 323 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Bifurcation and Symmetry by : BÖHMER

Download or read book Bifurcation and Symmetry written by BÖHMER and published by Birkhäuser. This book was released on 2013-03-08 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.

Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Author : Monica G. Cojocaru
Publisher : Springer
ISBN 13 : 3319123076
Total Pages : 538 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science by : Monica G. Cojocaru

Download or read book Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science written by Monica G. Cojocaru and published by Springer. This book was released on 2015-07-03 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26—30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics and its areas of applications.