Evolution Equations With A Complex Spatial Variable PDF Download
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| Author | : Ciprian G Gal |
| Publisher | : World Scientific |
| Total Pages | : 202 |
| Release | : 2014-03-18 |
| Genre | : Mathematics |
| ISBN | : 9814590614 |
Download Evolution Equations With A Complex Spatial Variable Book in PDF, ePub and Kindle
This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black-Merton-Scholes, Schrödinger and Korteweg-de Vries equations.The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought.For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane.
| Author | : Ciprian G. Gal |
| Publisher | : World Scientific Publishing Company Incorporated |
| Total Pages | : 191 |
| Release | : 2014 |
| Genre | : Mathematics |
| ISBN | : 9789814590594 |
Download Evolution Equations with a Complex Spatial Variable Book in PDF, ePub and Kindle
This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black Merton Scholes, Schr dinger and Korteweg de Vries equations. The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought. For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane.
| Author | : Sabir Umarov |
| Publisher | : Springer |
| Total Pages | : 446 |
| Release | : 2015-08-18 |
| Genre | : Mathematics |
| ISBN | : 3319207717 |
Download Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols Book in PDF, ePub and Kindle
The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.
| Author | : Yong-kui Chang |
| Publisher | : World Scientific |
| Total Pages | : 209 |
| Release | : 2022-07-13 |
| Genre | : Mathematics |
| ISBN | : 9811254370 |
Download Bloch-type Periodic Functions: Theory And Applications To Evolution Equations Book in PDF, ePub and Kindle
This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.
| Author | : Chin-yuan Lin |
| Publisher | : World Scientific |
| Total Pages | : 174 |
| Release | : 2014-08-08 |
| Genre | : Mathematics |
| ISBN | : 9814616400 |
Download An Exponential Function Approach To Parabolic Equations Book in PDF, ePub and Kindle
This volume is on initial-boundary value problems for parabolic partial differential equations of second order. It rewrites the problems as abstract Cauchy problems or evolution equations, and then solves them by the technique of elementary difference equations. Because of this, the volume assumes less background and provides an easy approach for readers to understand.
| Author | : Carolyn Murphy (Writer on mathematics) |
| Publisher | : Nova Science Publishers |
| Total Pages | : 105 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 9781536108736 |
Download Emerging Concepts in Evolution Equations Book in PDF, ePub and Kindle
This book reviews new research and analyzes emerging concepts in evolution equations. Chapter One discusses the evolution equation of Lie-type for finite deformations, and its time-discrete integration. Chapter Two presents a review of recent results on group analysis of nonlinear evolution equations in one spatial variable. Chapter Three addresses the problem of exponential stabilization of a class of 1-D PDEs with Dirichlet boundary control. (Imprint: Novinka)
| Author | : Aldo Belleni-morante |
| Publisher | : World Scientific |
| Total Pages | : 186 |
| Release | : 1994-05-18 |
| Genre | : Mathematics |
| ISBN | : 9813104570 |
Download A Concise Guide To Semigroups And Evolution Equations Book in PDF, ePub and Kindle
This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).
| Author | : George A Anastassiou |
| Publisher | : World Scientific |
| Total Pages | : 229 |
| Release | : 2015-06-23 |
| Genre | : Mathematics |
| ISBN | : 9814696110 |
Download Frontiers In Approximation Theory Book in PDF, ePub and Kindle
This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.
| Author | : John Michael Rassias |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 397 |
| Release | : 2017-03-20 |
| Genre | : Mathematics |
| ISBN | : 9813147628 |
Download Functional Equations And Inequalities: Solutions And Stability Results Book in PDF, ePub and Kindle
This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.
| Author | : Anastasios Mallios |
| Publisher | : World Scientific |
| Total Pages | : 302 |
| Release | : 2015-09-17 |
| Genre | : Mathematics |
| ISBN | : 981471948X |
Download Differential Sheaves And Connections: A Natural Approach To Physical Geometry Book in PDF, ePub and Kindle
This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.
