The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathema...
The Cauchy Problem for Hyperbolic Operators (Mathematical Topics S., v. 12)
by Karen Yagdjian
A construction of the fundamental solution to the Cauchy problem for hyperbolic operators with multiple characteristics is the target of this book. Investigations of the problem in various functional spaces and a propagation of singularities of the solutions are also presented. For operators with multiple characteristics, so-called Levy conditions play a crucial rule. Levy conditions described in the book allow the construction of fundamental solutions. A turning point theory for ordinary differ...
For a one-year, graduate-level course in Partial Differential Equations. Designed to bridge the gap between introductory texts in partial differential equations and the current literature in research journals, this text introduces students to the basics of classical PDEs and to a wide variety of more modern methods-especially the use of functional analysis-which has characterized much of the recent development of PDEs. Throughout, the results are almost completely self-contained.
Psicologia Positiva (Psicologia Geral, #1) (Psicologia General, #1)
by Max Krone
Elliptic Systems and Quasiconformal Mappings (Pure & Applied Mathematics S.)
by Heinrich Renelt
The primary aim of this text is to provide an explanation of those first order elliptic systems of partial differentiation equations in the plane whose solutions consist of the composition of an analytic function with a quasiconformal mapping. The text begins with an introductory chapter which covers necessary results on generalized derivatives, singular integral operators and other areas of analysis and measure theory. Explanations are then provided for such topics as the Bers-Nirenberg represe...
Finite Element Method (Dover Books on Engineering)
by Pin Tong and John N Rossettos
First-Order Partial Differential Equations, Vol. 1
by Hyun-ku Rhee, Rutherford Aris, and Neal R. Amundson
This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared...
Geometric Potential Analysis (Advances in Analysis and Geometry)
This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.
Inverse Problems for Partial Differential Equations (Applied Mathematical Sciences, #127)
by Victor Isakov
A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significan...
This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. It is a more modern, comprehensive treatment intended for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables, which is usually the only theoretical approach found in the majority of elementary textbooks. This will fill a need in the...
Solution Manual For Partial Differential Equations for Scientists and Engineers
by Stanley J Farlow
Approximate Solutions of Partial Differential Operators
by Todor V. Gramchev and Petar R. Popivanov
Microlocal analysis has been a fast developing field. In this book, the authors publish their research results in a summarized form. They deal with the following themes: asymptotic solutions for several classes of linear PDO with multiple characteristics; applications to microlocal solvability and hypoellipticity of the same classes of operators; solvability and hypoellipticity on the torus including construction of global parametrices; applications of the asymptotic methods and Gevrey microloca...
This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.
Handbook of Linear Partial Differential Equations for Engineers and Scientists
by Andrei D. Polyanin
Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. Parabolic, hyperbolic, and elliptic equations with constant and variable coefficients New exact solutions to linear equations and boundary value problems Equations and problems of general form that depend on arb...
Solve Partial Linear Differential Equations With Variables Coefficients
by Mohamed Tarek Hussein Mohamed Ouda
Practical Numerical Mathematics With Matlab: A Workbook And Solutions
by Myron Mike Sussman
This workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instruc...
Practical Numerical Mathematics With Matlab: Solutions
by Myron Mike Sussman
This workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instruc...
The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing concentration phenomena in physics and biology. While the two-dimensional theory is by now quite complete, the questions of global-in-time solvability and blowup characterization are largely open in higher dimensions. In this book, global-in-time solutions are constructed under (nearly) optimal assumptions on initial data and rigorous blowup criteria are derived.
The Theory and Applications of Iteration Methods (Systems Engineering, #4)
by Ioannis K Argyros and Ferenc Szidarovszky
The Theory and Applications of Iteration Methods focuses on an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. Each chapter presents new theoretical results and important applications in engineering, dynamic economic systems, and input-output systems. At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economics. Following an outline of general iteration schemes, the authors extend...
Bifurcation and Nonlinear Eigenvalue Problems (Lecture Notes in Mathematics, #782)
The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.