Strongly Coupled Parabolic and Elliptic Systems
Strongly Coupled Parabolic and Elliptic Systems

Author: Dung Le

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-11-05

Total Pages: 198

ISBN-13: 3110608766

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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

Regularity Results for Nonlinear Elliptic Systems and Applications
Regularity Results for Nonlinear Elliptic Systems and Applications

Author: Alain Bensoussan

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 450

ISBN-13: 3662129051

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This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.

Cross Diffusion Systems
Cross Diffusion Systems

Author: Dung Le

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-10-24

Total Pages: 236

ISBN-13: 3110795132

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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.

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

Author: Gershon Kresin

Publisher: American Mathematical Soc.

Published: 2012-08-15

Total Pages: 330

ISBN-13: 0821889818

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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.

Reaction Diffusion Systems
Reaction Diffusion Systems

Author: Gabriela Caristi

Publisher: CRC Press

Published: 2020-10-07

Total Pages: 428

ISBN-13: 1000117197

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"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."

Contributions to Nonlinear Elliptic Equations and Systems
Contributions to Nonlinear Elliptic Equations and Systems

Author: Alexandre N. Carvalho

Publisher: Birkhäuser

Published: 2015-11-14

Total Pages: 434

ISBN-13: 3319199021

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This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday. The articles it contains were born out of the ICMC Summer Meeting on Differential Equations – 2014 Chapter, also dedicated to de Figueiredo and held at the Universidade de São Paulo at São Carlos, Brazil from February 3-7, 2014. The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems. Djairo Guedes de Figueiredo has had a very active scientific career, publishing 29 monographs and over one hundred research articles. His influence on Brazilian mathematics has made him one of the pillars of the subject in that country. He had a major impact on the development of analysis, especially in its application to nonlinear elliptic partial differential equations and systems throughout the entire world. The articles collected here pay tribute to him and his legacy and are intended for graduate students and researchers in mathematics and related areas who are interested in nonlinear elliptic partial differential equations and systems.

Handbook of Differential Equations: Stationary Partial Differential Equations
Handbook of Differential Equations: Stationary Partial Differential Equations

Author: Michel Chipot

Publisher: Elsevier

Published: 2011-08-11

Total Pages: 618

ISBN-13: 0080560598

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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

Polyharmonic Boundary Value Problems
Polyharmonic Boundary Value Problems

Author: Filippo Gazzola

Publisher: Springer Science & Business Media

Published: 2010-06-03

Total Pages: 444

ISBN-13: 3642122442

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This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.

Mathematical Neuroscience
Mathematical Neuroscience

Author: Stanislaw Brzychczy

Publisher: Academic Press

Published: 2013-08-16

Total Pages: 201

ISBN-13: 0124104827

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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