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  • Fractional-in-Time Semilinear Parabolic Equations and Applications

    Collections series Mathematics and Statistics (R0)
    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. ... En savoir plus

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  • Evolution Equations With A Complex Spatial Variable

    Collections Livre 14 - Series On Concrete And Applicable Mathematics
    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 ... En savoir plus

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  • Complex Analysis

    In the Spirit of Lipman Bers

    Collections series Mathematics and Statistics (R0)
    This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has ... En savoir plus

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  • Numerical Methods for Partial Differential Equations

    Finite Difference and Finite Volume Methods

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    Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions ... En savoir plus

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  • Progress in Approximation Theory and Applicable Complex Analysis

    In Memory of Q.I. Rahman

    Collections series Mathematics and Statistics (R0)
    Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, ... En savoir plus

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  • Classical Fourier Analysis

    par Loukas Grafakos ...
    Collections series Mathematics and Statistics (R0)
    The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory ... En savoir plus

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  • Classical and Multilinear Harmonic Analysis: Volume 2

    Collections Livre 138 - Cambridge Studies in Advanced Mathematics
    This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert ... En savoir plus

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  • Handbook of Differential Geometry, Volume 1

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    In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. ... En savoir plus

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  • Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

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    Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing ... En savoir plus

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  • Partial Differential Equations: Methods, Applications And Theories

    par Harumi Hattori ...
    This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three ... En savoir plus

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  • L² Approaches in Several Complex Variables

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    par Takeo Ohsawa ...
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    The purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Highlighted are the new precise results on the L² extension of holomorphic functions.In Chapter 1, the classical questions of several complex variables motivating the ... En savoir plus

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