This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology.
Mixing elementary results and advanced methods, Algebraic Approach to Differential Equations aims to accustom differential equation specialists to algebraic methods in this area of interest.
The book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions.
This volume contains a selection of contributions by prominent mathematicians from the many interesting presentations delivered at the Conference of Mathematics and Mathematical Physics that was held in Fez, Morocco duing the period of 28-30 October, 2008.
This book provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations.
The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009.
Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on random factors.
This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrodinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations.
This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others.
This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set.
The book focuses on how to implement discrete wavelet transform methods in order to solve problems of reaction-diffusion equations and fractional-order differential equations that arise when modelling real physical phenomena.
This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China.
This book is a collection of lecture notes for the LIASFMA Hangzhou Autumn School on 'Control and Inverse Problems for Partial Differential Equations' which was held during October 17-22, 2016 at Zhejiang University, Hangzhou, China.
The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations.
The limit-point/limit-circle problem had its beginnings more than 100 years ago with the publication of Hermann Weyl's classic paper in Mathematische Annalen in 1910 on linear differential equations.
This unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1,000 examples.
This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm-Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations).
This invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations.
The volume contains a collection of original papers and surveys in various areas of Differential Equations, Control Theory and Optimization written by well-known specialists and is thus useful for PhD students and researchers in applied mathematics.
This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.
Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis).
This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem.
This book is an introductory course to the very important theory of distributions, as well as its applications in the resolution of partial differential equations (PDEs).
Applied Mathematics in Hydraulic Engineering is an excellent teaching guide and reference to treating nonlinear mathematical problems in hydraulic, hydrologic and coastal engineering.
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments.
This unique book is designed to provide the reader with an exposition of interesting aspects - encompassing both rudimentary and advanced knowledge - of oscillation theory of partial differential equations, which dates back to the publication in 1955 of a paper by Ph Hartman and A Wintner.
Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences.
During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).
New Edition: The Nonlinear Workbook (6th Edition)The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology.
This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle.
This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem.
Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth.
New Edition: The Nonlinear Workbook (6th Edition)The study of nonlinear dynamical systems has advanced tremendously in the last 15 years, making a big impact on science and technology.
