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On Stable Solutions Of Boundary Reaction Diffusion Equations And Applications To Nonlocal Problems With Neumann Data
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Book Synopsis On Stable Solutions of Boundary Reaction-diffusion Equations and Applications to Nonlocal Problems with Neumann Data by : Serena Dipierro
Download or read book On Stable Solutions of Boundary Reaction-diffusion Equations and Applications to Nonlocal Problems with Neumann Data written by Serena Dipierro and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar ́e-type inequality and classification results for stable solutions, and we apply them to the study of an associated nonlocal problem. We also establish a counterexample in the corresponding framework for the fractional Laplacian.
Book Synopsis Partial Differential Equations and Geometric Measure Theory by : Alessio Figalli
Download or read book Partial Differential Equations and Geometric Measure Theory written by Alessio Figalli and published by Springer. This book was released on 2018-05-23 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.
Book Synopsis Contemporary Research in Elliptic PDEs and Related Topics by : Serena Dipierro
Download or read book Contemporary Research in Elliptic PDEs and Related Topics written by Serena Dipierro and published by Springer. This book was released on 2019-07-12 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
Book Synopsis Nonlocal Diffusion Problems by : Fuensanta Andreu-Vaillo
Download or read book Nonlocal Diffusion Problems written by Fuensanta Andreu-Vaillo and published by American Mathematical Soc.. This book was released on 2010 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Reaction-diffusion Equations And Their Applications And Computational Aspects - Proceedings Of The China-japan Symposium by : Tatsien Li
Download or read book Reaction-diffusion Equations And Their Applications And Computational Aspects - Proceedings Of The China-japan Symposium written by Tatsien Li and published by World Scientific. This book was released on 1997-02-03 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the symposium was to provide a forum for presenting and discussing recent developments and trends in Reaction-diffusion Equations and to promote scientific exchanges among mathematicians in China and in Japan, especially for the younger generation. The topics discussed were: Layer dynamics, Traveling wave solutions and its stability, Equilibrium solutions and its limit behavior (stability), Bifurcation phenomena, Computational solutions, and Infinite dimensional dynamical system.
Book Synopsis Existence and Asymptotic Stability of a Periodic Solution with Boundary Layers of Reaction-diffusion Equations with Singularly Perturbed Neumann Boundary Conditions by :
Download or read book Existence and Asymptotic Stability of a Periodic Solution with Boundary Layers of Reaction-diffusion Equations with Singularly Perturbed Neumann Boundary Conditions written by and published by . This book was released on 2013 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Energy Methods for Free Boundary Problems by : S.N. Antontsev
Download or read book Energy Methods for Free Boundary Problems written by S.N. Antontsev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.
Book Synopsis Nonlocal and Abstract Parabolic Equations and Their Applications by : Piotr Mucha
Download or read book Nonlocal and Abstract Parabolic Equations and Their Applications written by Piotr Mucha and published by . This book was released on 2009 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :International Society for Analysis, Applications, and Computation. Congress Publisher :World Scientific ISBN 13 :9812794255 Total Pages :737 pages Book Rating :4.8/5 (127 download)
Book Synopsis Progress in Analysis by : International Society for Analysis, Applications, and Computation. Congress
Download or read book Progress in Analysis written by International Society for Analysis, Applications, and Computation. Congress and published by World Scientific. This book was released on 2003-01-01 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting. Contents: .: Volume 1: Function Spaces and Fractional Calculus (V I Burenkov & S Samko); Asymptotic Decomposition (Methods of Small Parameters, Averaging Theory) (J A Dubinski); Integral Transforms and Applications (S Saitoh et al.); Analytic Functionals, Hyperfunctions and Generalized Functions (M Morimoto & H Komatsu); Geometric Function Theory (G Kohr & M Kohr); omplex Function Spaces (R Aulaskari & I Laine); Value Distribution Theory and Complex Dynamics (C C Yang); Clifford Analysis (K Grlebeck et al.); Octonions (T Dray & C Monogue); Nonlinear Potential Theory (O Martio); Classical and Fine Potential Theory, Holomorphic and Finely Holomorphic Functions (P Tamrazov); Differential Geometry and Control Theory for PDEs (B Gulliver et al.); Differential Geometry and Quantum Physics (-); Dynamical Systems (B Fiedler); Attractors for Partial Differential Equations (G Raugel); Spectral Theory of Differential Operators (B Vainberg); Pseudodifferential Operators, Quantization and Signal Analysis (M W Wong); Microlocal Analysis (B-W Schulze & M Korey); Volume 2: Complex and Functional Analytic Methods in PDEs (A Cialdea et al.); Geometric Properties of Solutions of PDEs (R Magnanini); Qualitative Properties of Solutions of Hyperbolic and SchrAdinger Equations (M Reissig & K Yagdjian); Homogenization Moving Boundaries and Porous Media (A Bourgeat & R P Gilbert); Constructive Methods in Applied Problems (P Krutitskii); Waves in Complex Media (R P Gilbert & A Wirgin); Nonlinear Waves (I Lasiecka & H Koch); Mathematical Analysis of Problems in Solid Mechanics (K Hackl & X Li); Direct and Inverse Scattering (L Fishman); Inverse Problems (G N Makrakis et al.); Mathematical Methods in Non-Destructive Evaluation and Non-Destructive Testing (A Wirgin); Numerical Methods for PDEs, Systems and Optimization (A Ben-Israel & I Herrera). Readership: Graduate students and researchers in real, complex, numerical analysis, as well as mathematical physics."
Book Synopsis The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise by : Arnaud Debussche
Download or read book The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise written by Arnaud Debussche and published by Springer. This book was released on 2013-10-01 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.
Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States II by : W.-M. Ni
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.
Book Synopsis Global Stability of Stationary Solutions of Reaction-Diffusion System by : Robert A. Gardner
Download or read book Global Stability of Stationary Solutions of Reaction-Diffusion System written by Robert A. Gardner and published by . This book was released on 1979 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: A condition is given which implies that the trivial solution, U is identically equal to O, of a class of reaction-diffusion systems with homogenous Dirichlet boundary conditions, is a global attractor for all non-negative solutions. In certain cases, this condition, which relates the diffusion matrix and the domain to a parameter which depends on the nonlinear term, significantly improves similar conditions which can be obtained from energy estimates. Applications are given to equations arising in mathematical ecology.
Book Synopsis Nonlinear PDE’s in Condensed Matter and Reactive Flows by : Henri Berestycki
Download or read book Nonlinear PDE’s in Condensed Matter and Reactive Flows written by Henri Berestycki and published by Springer Science & Business Media. This book was released on 2002-11-30 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.
Book Synopsis Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions by : José Antonio Carrillo
Download or read book Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions written by José Antonio Carrillo and published by Springer. This book was released on 2017-10-03 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fuzzy Systems and Data Mining IX by : A.J. Tallón-Ballesteros
Download or read book Fuzzy Systems and Data Mining IX written by A.J. Tallón-Ballesteros and published by IOS Press. This book was released on 2023-12-19 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy systems and data mining are indispensible aspects of the digital technology on which we now all depend. Fuzzy logic is intrinsic to applications in the electrical, chemical and engineering industries, and also in the fields of management and environmental issues. Data mining is indispensible in dealing with big data, massive data, and scalable, parallel and distributed algorithms. This book presents the proceedings of FSDM 2023, the 9th International Conference on Fuzzy Systems and Data Mining, held from 10-13 November 2023 as a hybrid event, with some participants attending in Chongqing, China, and others online. The conference focuses on four main areas: fuzzy theory, algorithms and systems; fuzzy application; data mining; and the interdisciplinary field of fuzzy logic and data mining, and provides a forum for experts, researchers, academics and representatives from industry to share the latest advances in the field of fuzzy sets and data mining. This year, topics from two special sessions on granular-ball computing and the application of generative AI, as well as machine learning and neural networks, were also covered. A total of 363 submissions were received, and after careful review by the members of the international program committee, 110 papers were accepted for presentation at the conference and publication here, representing an acceptance rate of just over 30%. Covering a comprehensive range of current research and developments in fuzzy logic and data mining, the book will be of interest to all those working in the field of data science.
Download or read book Nonlocal Diffusion Problems written by and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
