Nonlocal Diffusion Problems
Nonlocal Diffusion Problems

Author: Fuensanta Andreu-Vaillo

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 274

ISBN-13: 0821852302

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Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.

Non-Local Partial Differential Equations for Engineering and Biology
Non-Local Partial Differential Equations for Engineering and Biology

Author: Nikos I. Kavallaris

Publisher: Springer

Published: 2017-11-28

Total Pages: 310

ISBN-13: 3319679449

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This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.

Trends in Nonlinear Analysis
Trends in Nonlinear Analysis

Author: Markus Kirkilionis

Publisher: Springer Science & Business Media

Published: 2002-11-27

Total Pages: 446

ISBN-13: 9783540441984

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Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.

Delay Differential Equations
Delay Differential Equations

Author: Yang Kuang

Publisher: Academic Press

Published: 1993-03-05

Total Pages: 413

ISBN-13: 0080960022

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Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems. The book treats both autonomous and nonautonomous systems with various delays. Key topics addressed are the possible delay influence on the dynamics of the system, such as stability switching as time delay increases, the long time coexistence of populations, and the oscillatory aspects of the dynamics. The book also includes coverage of the interplay of spatial diffusion and time delays in some diffusive delay population models. The treatment presented in this monograph will be of great value in the study of various classes of DDEs and their multidisciplinary applications.

Bifurcation Theory of Functional Differential Equations
Bifurcation Theory of Functional Differential Equations

Author: Shangjiang Guo

Publisher: Springer Science & Business Media

Published: 2013-07-30

Total Pages: 295

ISBN-13: 1461469929

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This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).

Traveling Wave Solutions of Parabolic Systems
Traveling Wave Solutions of Parabolic Systems

Author: A. I. Volpert

Publisher: American Mathematical Soc.

Published:

Total Pages: 474

ISBN-13: 9780821897577

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The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.

Encyclopedia of Energy, Natural Resource, and Environmental Economics
Encyclopedia of Energy, Natural Resource, and Environmental Economics

Author:

Publisher: Newnes

Published: 2013-03-29

Total Pages: 1056

ISBN-13: 0080964524

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Every decision about energy involves its price and cost. The price of gasoline and the cost of buying from foreign producers; the price of nuclear and hydroelectricity and the costs to our ecosystems; the price of electricity from coal-fired plants and the cost to the atmosphere. Giving life to inventions, lifestyle changes, geopolitical shifts, and things in-between, energy economics is of high interest to Academia, Corporations and Governments. For economists, energy economics is one of three subdisciplines which, taken together, compose an economic approach to the exploitation and preservation of natural resources: energy economics, which focuses on energy-related subjects such as renewable energy, hydropower, nuclear power, and the political economy of energy resource economics, which covers subjects in land and water use, such as mining, fisheries, agriculture, and forests environmental economics, which takes a broader view of natural resources through economic concepts such as risk, valuation, regulation, and distribution Although the three are closely related, they are not often presented as an integrated whole. This Encyclopedia has done just that by unifying these fields into a high-quality and unique overview. The only reference work that codifies the relationships among the three subdisciplines: energy economics, resource economics and environmental economics. Understanding these relationships just became simpler! Nobel Prize Winning Editor-in-Chief (joint recipient 2007 Peace Prize), Jason Shogren, has demonstrated excellent team work again, by coordinating and steering his Editorial Board to produce a cohesive work that guides the user seamlessly through the diverse topics This work contains in equal parts information from and about business, academic, and government perspectives and is intended to serve as a tool for unifying and systematizing research and analysis in business, universities, and government

Non-Local Cell Adhesion Models
Non-Local Cell Adhesion Models

Author: Andreas Buttenschön

Publisher: Springer Nature

Published: 2021-06-09

Total Pages: 152

ISBN-13: 3030671119

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This monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models. The novel aspect is the non-local term (an integral operator), which accounts for forces generated by long ranged cell interactions. The analysis of non-local models has started only recently, and it has become a vibrant area of applied mathematics. This monograph contributes a systematic analysis of steady states and their bifurcation structure, combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the symmetries of the non-local term. These methods allow readers to analyze and understand cell adhesion on a deep level.