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Blow Up Theories For Semilinear Parabolic Equations
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Book Synopsis Blow-up Theories for Semilinear Parabolic Equations by : Bei Hu
Download or read book Blow-up Theories for Semilinear Parabolic Equations written by Bei Hu and published by Springer Science & Business Media. This book was released on 2011-03-23 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.
Book Synopsis Geometric Theory of Semilinear Parabolic Equations by :
Download or read book Geometric Theory of Semilinear Parabolic Equations written by and published by . This book was released on 1983 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Theory of Semilinear Parabolic Equations by : Daniel Henry
Download or read book Geometric Theory of Semilinear Parabolic Equations written by Daniel Henry and published by . This book was released on 2014-01-15 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations by : Victor A. Galaktionov
Download or read book Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations written by Victor A. Galaktionov and published by CRC Press. This book was released on 2014-09-22 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book
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.
Book Synopsis Nonlinear Second Order Parabolic Equations by : Mingxin Wang
Download or read book Nonlinear Second Order Parabolic Equations written by Mingxin Wang and published by CRC Press. This book was released on 2021-04-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The parabolic partial differential equations model one of the most important processes in the real-world: diffusion. Whether it is the diffusion of energy in space-time, the diffusion of species in ecology, the diffusion of chemicals in biochemical processes, or the diffusion of information in social networks, diffusion processes are ubiquitous and crucial in the physical and natural world as well as our everyday lives. This book is self-contained and covers key topics such as theory and Schauder theory, maximum principle, comparison principle, regularity and uniform estimates, initial-boundary value problems of semilinear parabolic scalar equations and weakly coupled parabolic systems, the upper and lower solutions method, monotone properties and long-time behaviours of solutions, convergence of solutions and stability of equilibrium solutions, global solutions and finite time blowup. It also touches on periodic boundary value problems, free boundary problems, and semigroup theory. The book covers major theories and methods of the field, including topics that are useful but hard to find elsewhere. This book is based on tried and tested teaching materials used at the Harbin Institute of Technology over the past ten years. Special care was taken to make the book suitable for classroom teaching as well as for self-study among graduate students. About the Author: Mingxin Wang is Professor of Mathematics at Harbin Institute of Technology, China. He has published ten monographs and textbooks and 260 papers. He is also a supervisor of 30 PhD students.
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.
Book Synopsis Time Optimal Control of Evolution Equations by : Gengsheng Wang
Download or read book Time Optimal Control of Evolution Equations written by Gengsheng Wang and published by Springer. This book was released on 2018-08-22 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal control problems. By discussing the best way of representing various control problems and equivalence among them, this systematic study gives readers the tools they need to solve practical problems in control. After introducing preliminaries in functional analysis, evolution equations, and controllability and observability estimates, the authors present their time-optimal control framework, which consists of four elements: a controlled system, a control constraint set, a starting set, and an ending set. From there, they use their framework to address areas of recent development in time-optimal control, including the existence of admissible controls and optimal controls, Pontryagin’s maximum principle for optimal controls, the equivalence of different optimal control problems, and bang-bang properties. This monograph will appeal to researchers and graduate students in time-optimal control theory, as well as related areas of controllability and dynamic programming. For ease of reference, the text itself is self-contained on the topic of time-optimal control. Frequent examples throughout clarify the applications of theorems and definitions, although experience with functional analysis and differential equations will be useful.
Book Synopsis Partial Differential Equations and Applications by : Hong-Ming Yin
Download or read book Partial Differential Equations and Applications written by Hong-Ming Yin and published by Elsevier. This book was released on 2023-06-28 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Sciences offers a unique approach to this key subject by connecting mathematical principles to the latest research advances in select topics. Beginning with very elementary PDEs, such as classical heat equations, wave equations and Laplace equations, the book focuses on concrete examples. It gives students basic skills and techniques to find explicit solutions for partial differential equations. As it progresses, the book covers more advanced topics such as the maximum principle and applications, Green’s representation, Schauder’s theory, finite-time blowup, and shock waves. By exploring these topics, students gain the necessary tools to deal with research topics in their own fields, whether proceeding in math or engineering areas. Class tested over multiple years with advanced undergraduate and graduate courses Features many concrete examples and chapter exercises Appropriate for advanced undergraduate and graduate courses geared to math and engineering students Requires minimal background beyond advanced calculus and differential equations
Book Synopsis Fractional-in-Time Semilinear Parabolic Equations and Applications by : Ciprian G. Gal
Download or read book Fractional-in-Time Semilinear Parabolic Equations and Applications written by Ciprian G. Gal and published by Springer Nature. This book was released on 2020-09-23 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics. Besides classical examples involving the Laplace operator, subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov) boundary conditions, the framework also includes non-standard diffusion operators of "fractional" type, subject to appropriate boundary conditions. This book is aimed at graduate students and researchers in mathematics, physics, mathematical engineering and mathematical biology, whose research involves partial differential equations.
Book Synopsis Frontiers in Industrial and Applied Mathematics by : Rajesh Kumar Sharma
Download or read book Frontiers in Industrial and Applied Mathematics written by Rajesh Kumar Sharma and published by Springer Nature. This book was released on 2023-02-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21–22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.
Book Synopsis Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model by : Takashi Suzuki
Download or read book Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model written by Takashi Suzuki and published by Springer. This book was released on 2015-11-19 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Book Synopsis Generalized Functions and Fourier Analysis by : Michael Oberguggenberger
Download or read book Generalized Functions and Fourier Analysis written by Michael Oberguggenberger and published by Birkhäuser. This book was released on 2017-05-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.
Book Synopsis Semilinear Elliptic Equations by : Takashi Suzuki
Download or read book Semilinear Elliptic Equations written by Takashi Suzuki and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-12 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.
Book Synopsis Nonlinear Second Order Parabolic Equations by : Mingxin Wang
Download or read book Nonlinear Second Order Parabolic Equations written by Mingxin Wang and published by CRC Press. This book was released on 2021-05-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The parabolic partial differential equations model one of the most important processes in the real-world: diffusion. Whether it is the diffusion of energy in space-time, the diffusion of species in ecology, the diffusion of chemicals in biochemical processes, or the diffusion of information in social networks, diffusion processes are ubiquitous and crucial in the physical and natural world as well as our everyday lives. This book is self-contained and covers key topics such as the Lp theory and Schauder theory, maximum principle, comparison principle, regularity and uniform estimates, initial-boundary value problems of semilinear parabolic scalar equations and weakly coupled parabolic systems, the upper and lower solutions method, monotone properties and long-time behaviours of solutions, convergence of solutions and stability of equilibrium solutions, global solutions and finite time blowup. It also touches on periodic boundary value problems, free boundary problems, and semigroup theory. The book covers major theories and methods of the field, including topics that are useful but hard to find elsewhere. This book is based on tried and tested teaching materials used at the Harbin Institute of Technology over the past ten years. Special care was taken to make the book suitable for classroom teaching as well as for self-study among graduate students. About the Author: Mingxin Wang is Professor of Mathematics at Harbin Institute of Technology, China. He has published ten monographs and textbooks and 260 papers. He is also a supervisor of 30 PhD students.
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.
Book Synopsis MEAN FIELD THEORIES AND DUAL VARIATION by : Takashi Suzuki
Download or read book MEAN FIELD THEORIES AND DUAL VARIATION written by Takashi Suzuki and published by Springer Science & Business Media. This book was released on 2009-01-01 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.
