The Heat Equation With Singular Nonlinearity And Singular Initial Data

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Patterns of Dynamics

Author : Pavel Gurevich
Publisher : Springer
ISBN 13 : 3319641735
Total Pages : 411 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Patterns of Dynamics by : Pavel Gurevich

Download or read book Patterns of Dynamics written by Pavel Gurevich and published by Springer. This book was released on 2018-02-07 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes.

Nonlinear Evolution Equations - Global Behavior of Solutions

Author : Alain Haraux
Publisher : Springer
ISBN 13 : 3540385347
Total Pages : 324 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Nonlinear Evolution Equations - Global Behavior of Solutions by : Alain Haraux

Download or read book Nonlinear Evolution Equations - Global Behavior of Solutions written by Alain Haraux and published by Springer. This book was released on 2006-11-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics for Nonlinear Phenomena — Analysis and Computation

Author : Yasunori Maekawa
Publisher : Springer
ISBN 13 : 3319667645
Total Pages : 335 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Mathematics for Nonlinear Phenomena — Analysis and Computation by : Yasunori Maekawa

Download or read book Mathematics for Nonlinear Phenomena — Analysis and Computation written by Yasunori Maekawa and published by Springer. This book was released on 2017-11-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.

Analysis and Topology in Nonlinear Differential Equations

Author : Djairo G de Figueiredo
Publisher : Springer
ISBN 13 : 3319042149
Total Pages : 465 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Analysis and Topology in Nonlinear Differential Equations by : Djairo G de Figueiredo

Download or read book Analysis and Topology in Nonlinear Differential Equations written by Djairo G de Figueiredo and published by Springer. This book was released on 2014-06-16 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical devices.

Nonlinear Evolution Equations and Related Topics

Author : Wolfgang Arendt
Publisher : Springer Science & Business Media
ISBN 13 : 9783764371074
Total Pages : 844 pages
Book Rating : 4.3/5 (71 download)

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Book Synopsis Nonlinear Evolution Equations and Related Topics by : Wolfgang Arendt

Download or read book Nonlinear Evolution Equations and Related Topics written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2004-08-20 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.

Non-Local Partial Differential Equations for Engineering and Biology

Author : Nikos I. Kavallaris
Publisher : Springer
ISBN 13 : 3319679449
Total Pages : 310 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Non-Local Partial Differential Equations for Engineering and Biology by : Nikos I. Kavallaris

Download or read book Non-Local Partial Differential Equations for Engineering and Biology written by Nikos I. Kavallaris and published by Springer. This book was released on 2017-11-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Mathematical Fluid Dynamics

Author : S. Friedlander
Publisher : Gulf Professional Publishing
ISBN 13 : 008053354X
Total Pages : 627 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Mathematical Fluid Dynamics by : S. Friedlander

Download or read book Handbook of Mathematical Fluid Dynamics written by S. Friedlander and published by Gulf Professional Publishing. This book was released on 2003-03-27 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Evolution Equations, Semigroups and Functional Analysis

Author : Alfredo Lorenzi
Publisher : Birkhäuser
ISBN 13 : 3034882211
Total Pages : 404 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Evolution Equations, Semigroups and Functional Analysis by : Alfredo Lorenzi

Download or read book Evolution Equations, Semigroups and Functional Analysis written by Alfredo Lorenzi and published by Birkhäuser. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi.

Equadiff 2003 - Proceedings Of The International Conference On Differential Equations

Author : Freddy Dumortier
Publisher : World Scientific
ISBN 13 : 9814480916
Total Pages : 1180 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Equadiff 2003 - Proceedings Of The International Conference On Differential Equations by : Freddy Dumortier

Download or read book Equadiff 2003 - Proceedings Of The International Conference On Differential Equations written by Freddy Dumortier and published by World Scientific. This book was released on 2005-02-23 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view.A broad range of topics are treated through contributions by leading experts of their fields, presenting the most recent developments. A large variety of techniques are being used, stressing geometric, topological, ergodic and numerical aspects.The scope of the book is wide, ranging from pure mathematics to various applied fields. Examples of the latter are provided by subjects from earth and life sciences, classical mechanics and quantum-mechanics, among others.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

2018 MATRIX Annals

Author : Jan de Gier
Publisher : Springer Nature
ISBN 13 : 3030382303
Total Pages : 430 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis 2018 MATRIX Annals by : Jan de Gier

Download or read book 2018 MATRIX Annals written by Jan de Gier and published by Springer Nature. This book was released on 2020-04-07 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in 2018: - Non-Equilibrium Systems and Special Functions - Algebraic Geometry, Approximation and Optimisation - On the Frontiers of High Dimensional Computation - Month of Mathematical Biology - Dynamics, Foliations, and Geometry In Dimension 3 - Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type - Functional Data Analysis and Beyond - Geometric and Categorical Representation Theory The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Smoothing and Decay Estimates for Nonlinear Diffusion Equations

Author : Juan Luis Vázquez
Publisher : OUP Oxford
ISBN 13 : 0191525251
Total Pages : 248 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Smoothing and Decay Estimates for Nonlinear Diffusion Equations by : Juan Luis Vázquez

Download or read book Smoothing and Decay Estimates for Nonlinear Diffusion Equations written by Juan Luis Vázquez and published by OUP Oxford. This book was released on 2006-08-03 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis. Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porous medium type"), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity.

On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation

Author : Charles Collot
Publisher : American Mathematical Soc.
ISBN 13 : 1470436264
Total Pages : 110 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation by : Charles Collot

Download or read book On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation written by Charles Collot and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the energy super critical semilinear heat equation The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.

Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

Author : Victor A. Galaktionov
Publisher : CRC Press
ISBN 13 : 0203998065
Total Pages : 383 pages
Book Rating : 4.2/5 (39 download)

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Book Synopsis Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications by : Victor A. Galaktionov

Download or read book Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications written by Victor A. Galaktionov and published by CRC Press. This book was released on 2004-05-24 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Plya in the 1930's and rediscovered in part several times since, it was not un

Handbook of Differential Equations: Evolutionary Equations

Author : C.M. Dafermos
Publisher : Elsevier
ISBN 13 : 0080461387
Total Pages : 677 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Differential Equations: Evolutionary Equations by : C.M. Dafermos

Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2005-10-05 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.. Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.

Geometric Properties for Parabolic and Elliptic PDE's

Author : Vincenzo Ferone
Publisher : Springer Nature
ISBN 13 : 3030733637
Total Pages : 303 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Geometric Properties for Parabolic and Elliptic PDE's by : Vincenzo Ferone

Download or read book Geometric Properties for Parabolic and Elliptic PDE's written by Vincenzo Ferone and published by Springer Nature. This book was released on 2021-06-12 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20–24, 2019. This book will be of great interest for the mathematical community and in particular for researchers studying parabolic and elliptic PDEs. It covers many different fields of current research as follows: convexity of solutions to PDEs, qualitative properties of solutions to parabolic equations, overdetermined problems, inverse problems, Brunn-Minkowski inequalities, Sobolev inequalities, and isoperimetric inequalities.

Numerical Methods and Applications

Author : Lirkov Ivan Dimov
Publisher : Springer
ISBN 13 : 3642184669
Total Pages : 524 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Numerical Methods and Applications by : Lirkov Ivan Dimov

Download or read book Numerical Methods and Applications written by Lirkov Ivan Dimov and published by Springer. This book was released on 2011-01-27 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Numerical Methods and Applications, NMA 2010, held in Borovets, Bulgaria, in August 2010. The 60 revised full papers presented together with 3 invited papers were carefully reviewed and selected from numerous submissions for inclusion in this book. The papers are organized in topical sections on Monte Carlo and quasi-Monte Carlo methods, environmental modeling, grid computing and applications, metaheuristics for optimization problems, and modeling and simulation of electrochemical processes.

Superlinear Parabolic Problems

Author : Pavol Quittner
Publisher : Springer Science & Business Media
ISBN 13 : 3764384425
Total Pages : 593 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Superlinear Parabolic Problems by : Pavol Quittner

Download or read book Superlinear Parabolic Problems written by Pavol Quittner and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 593 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 book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.