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Fractional-in-Time Semilinear Parabolic Equations and Applications

Author: Ciprian G. Gal

Publisher: Springer Nature

Published: 2020-09-23

Total Pages: 193

ISBN-13: 3030450430

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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 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.

Fractional Differential Equations

Author: Bangti Jin

Publisher: Springer Nature

Published: 2021-07-22

Total Pages: 377

ISBN-13: 303076043X

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This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.

Book Synopsis Fractional Differential Equations by : Bangti Jin

Download or read book Fractional Differential Equations written by Bangti Jin and published by Springer Nature. This book was released on 2021-07-22 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.

Fractional Dispersive Models and Applications

Author: Panayotis G. Kevrekidis

Publisher: Springer Nature

Published:

Total Pages: 337

ISBN-13: 3031549783

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Book Synopsis Fractional Dispersive Models and Applications by : Panayotis G. Kevrekidis

Download or read book Fractional Dispersive Models and Applications written by Panayotis G. Kevrekidis and published by Springer Nature. This book was released on with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fractional Differential Equations

Author: Anatoly Kochubei

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-02-19

Total Pages: 528

ISBN-13: 3110571668

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This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.

Book Synopsis Fractional Differential Equations by : Anatoly Kochubei

Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.

Numerical Control: Part A

Author:

Publisher: Elsevier

Published: 2022-02-15

Total Pages: 596

ISBN-13: 0323853390

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Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control

Book Synopsis Numerical Control: Part A by :

Download or read book Numerical Control: Part A written by and published by Elsevier. This book was released on 2022-02-15 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control

Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations

Author: Sergey I Piskarev

Publisher: World Scientific

Published: 2023-07-05

Total Pages: 213

ISBN-13: 9811272794

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The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.

Book Synopsis Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations by : Sergey I Piskarev

Download or read book Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations written by Sergey I Piskarev and published by World Scientific. This book was released on 2023-07-05 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.

Numerical Treatment and Analysis of Time-Fractional Evolution Equations

Author: Bangti Jin

Publisher: Springer Nature

Published: 2023-02-26

Total Pages: 428

ISBN-13: 3031210506

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This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis.

Book Synopsis Numerical Treatment and Analysis of Time-Fractional Evolution Equations by : Bangti Jin

Download or read book Numerical Treatment and Analysis of Time-Fractional Evolution Equations written by Bangti Jin and published by Springer Nature. This book was released on 2023-02-26 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis.

Numerical Methods and Applications

Author: Ivan Georgiev

Publisher: Springer Nature

Published: 2023-05-15

Total Pages: 365

ISBN-13: 3031324129

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This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications, NMA 2022, held in Borovets, Bulgaria, in August 2022.The 30 revised regular papers presented were carefully reviewed and selected from 38 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.

Book Synopsis Numerical Methods and Applications by : Ivan Georgiev

Download or read book Numerical Methods and Applications written by Ivan Georgiev and published by Springer Nature. This book was released on 2023-05-15 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications, NMA 2022, held in Borovets, Bulgaria, in August 2022.The 30 revised regular papers presented were carefully reviewed and selected from 38 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.

Complicated Dynamics in Scalar Semilinear Parabolic Equations in Higher Space Dimension

Author: University of Minnesota. Institute for Mathematics and Its Applications

Publisher:

Published: 1990

Total Pages: 26

ISBN-13:

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Book Synopsis Complicated Dynamics in Scalar Semilinear Parabolic Equations in Higher Space Dimension by : University of Minnesota. Institute for Mathematics and Its Applications

Download or read book Complicated Dynamics in Scalar Semilinear Parabolic Equations in Higher Space Dimension written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1990 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Methods and Applications

Author: Geno Nikolov

Publisher: Springer

Published: 2019-01-21

Total Pages: 500

ISBN-13: 3030106926

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This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Numerical Methods and Applications, NMA 2018, held in Borovets, Bulgaria, in August 2018. The 56 revised regular papers presented were carefully reviewed and selected from 61 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.

Book Synopsis Numerical Methods and Applications by : Geno Nikolov

Download or read book Numerical Methods and Applications written by Geno Nikolov and published by Springer. This book was released on 2019-01-21 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Numerical Methods and Applications, NMA 2018, held in Borovets, Bulgaria, in August 2018. The 56 revised regular papers presented were carefully reviewed and selected from 61 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.