Springer, 2025. — 508 p. This volume compiles selected papers focusing on the applications of differential equations across various scientific domains, presented at the International Conference "New Trends in the Applications of Differential Equations in Sciences" (NTADES), which took place in Saints Constantine and Helena, Bulgaria, in July 2024. The book is organized around...
Basel: Birkhäuser, 2025. — 961 p. This book provides a comprehensive and self-contained introduction to the study of the Cauchy problem and unique continuation properties for partial differential equations. Aimed at graduate and advanced undergraduate students, it bridges foundational concepts such as Lebesgue measure theory, functional analysis, and partial differential...
М.: Ленанд, 2018. — 256 с. — (Школа Опойцева). Книга отличается краткостью и прозрачностью изложения, вплоть до объяснений «на пальцах». Значительное внимание уделяется мотивации результатов и укрупненному видению. Помимо обычной для дифференциальных уравнений тематики рассматриваются: бифуркации и катастрофы, аттракторы и детерминированный хаос. Излагается теория устойчивости,...
Zishka Publishing, 2022. — 160 p. — ISBN: 978-1-941691-39-7. This workbook on ordinary differential equations serves either as a handy supplement to current students or as a useful review for students who have previously studied the material. This book focuses on essential techniques for solving and understanding differential equations. Topics include: first-order differential...
Springer, 2024. — 197 p. This book is focused on modeling with linear differential equations with constant coefficients. The author starts with the elementary natural growth equation and ends with the heat equation on the real line. The emphasis is on linear algebra, Fourier theory, and specifically data analysis, which is given a very prominent role and is often the book's...
De Gruyter, 2024. — 472 p. This book presents a projector analysis of dynamic systems on time scales. The dynamic systems are classified as first, second, third and fourth kinds. For each classes of dynamic systems the basic matrix chains are constructed. The proposed theory is applied for decoupling of dynamic equations on time scales. Properly involved derivatives,...
Infinity Books, 2023. — 494 p. Preface. The Laplace Transform. Introduction. Further Properties and Initial-Value Problems. Convolutions and Generalized Functions. Table of Laplace Transforms. Series Solutions of Ordinary Differential Eqs. Basic Concepts. Solutions About Ordinary Points. Solutions About Regular Singular Points. Cauchy-Euler Equations. The General Equation y′′ +...
Springer, 1992. — 226 p. In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in...
Paris: Société Mathématique de France, 2017. — 216 p. We study a variant of the Alt, Caffarelli, and Friedman free boundary problem, with many phases and a slightly different volume term, which we originally designed to guess the localization of eigenfunctions of a Schrödinger operator in a domain. We prove Lipschitz bounds for the functions and some nondegeneracy and...
Paris: Société Mathématique de France, 2023. — 152 p. Motivation and a general overview of the main results Motivation Additional historical comments A rough outline of the main assumptions and results Our assumptions Some examples where our assumptions hold Classical elliptic operators Ahlfors regular sets Caffarelli and Sylvestre fractional operators Sawtooth domains Balls...
WSPC, 2024. — 414 p. Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena. In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years,...
Elsevier, Academic Press, 1994. — 446 p. Dedication Foreword General Existence of Solutions Theory Introduction Approximation of Solutions of Continuous Nonlinear PDEs Spaces of Generalized Functions Extending T(x, D) to the Order Completion of Spaces of Smooth Functions Existence of Generalized Solutions A Few First Examples Generalized Solutions as Measurable Functions...
Basel: Birkhäuser, 2024. — 262 p. This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first “Workshop on Systems Theory and PDEs” (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include:...
Cham: Springer Nature Switzerland, 2024. — 143 p. Introducing a groundbreaking framework for stochastic partial differential equations (SPDEs), this work presents three significant advancements over the traditional variational approach. Firstly, Stratonovich SPDEs are explicitly addressed. Widely used in physics, Stratonovich SPDEs have typically been converted to Ito form for...
North Holland, 1980. — 339 p. Sequential Solutions of Nonlinear PDEs Necessary and/or Sufficient Conditions for the Existence of Sequential Solutions Algebras Containing the Distribution Resolution of Singularities of Weak Solutions for Polynomial Nonlinear PDEs Stability and Exactness of Sequential and Weak Solutions for Polynomial Nonlinear PDEs Characterization of the...
Springer, 2024. — 597 p. This book studies the theoretical aspects for a variety of coupled fractional differential systems involving Riemann-Liouville, Caputo, ψ-Riemann--Liouville, Hilfer, ψ--Hilfer, Hadamard, Hilfer--Hadamard, Erdelyi--Kober, (k, ψ)-Hilfer, generalized, Proportional, ψ-Proportional, Hilfer--proportional, ψ-Hilfer--proportional type fractional derivative...
Boca Raton: CRC Press, 2024. — 243 p. Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and...
Basel: Birkhäuser, 2004. — 350 p. Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2003. This book contains a detailed mathematical analysis of the variational approach to image restoration based on the minimization of the total variation submitted to the constraints given by the image acquisition model. This model, initially introduced by Rudin, Osher, and Fatemi,...
Basel: Birkhäuser, 2012. — 349 p. This book details the mathematical developments in total variation based image restauration. This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters...The book is written with...
Boca Raton: CRC Press, 2024. — 452 p. Preface About the authors Introduction Linear PDEs Separation of Variables Method Symmetric Differential Operators Fourier Analysis Eigenfunction Expansion Method Special Functions Cylindrical and Spherical BVPs Bibliography Subject Index Index of Capsule Biographies
Springer Nature Singapore, 2024. — 153 p. This book are notes prepared for the PhD courses that the author has been teaching during the last 10 years. The material available in the already existing literature (papers and essays) has been collected in this unique text, presenting the results with all the details for the reader’s convenience, fixing a unified notation, and...
WSPC, 2024. — 283 p. Review of the First Edition: "The monograph is well written and organized and recommended to graduate students and researchers in applied mathematics or engineering." Zentralblatt MATH The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with...
Springer, 2024. — 180 p. Preface A Short Introduction to Reduced Basis Method Worked Out Problems for Beginners: Steady Cases Worked Out Problem 1: Steady Heat Conduction in a Thermal Block Worked Out Problem 2: A Linear Elasticity Problem on a Square Worked Out Problem 3: Thermal Transfer Problem in a Parametrized Geometry Worked Out Problem 4: A Transport Problem for the 2D...
Laxmi Publications, 2021. — 201 p. Geometrical Meaning of a Differential Equation Exact Differential Equations Differential Equations of the First Order and Higher Degree Singular Solutions Orthogonal Trajectories Linear Differential Equations with Constant Coefficients Homogeneous Linear Ordinary Differential Equations Total Differential Equations Linear Differential Equations...
Laxmi Publications, 2021. — 412 p. Series Solution of Differential Equations Legendre Equation Bessel Equation Hypergeometric Equation Sturm-Liouville Problems Partial Differential Equations 7. Partial Differential Equations of the First Order (Equations Linear in p and q) Partial Differential Equations of the First Order (Equations Non-linear in p and q) Homogeneous Linear...
Boca Raton: CRC Press, 2024. — 334 p. "Regularity Techniques for Elliptic PDEs and the Fractional Laplacian" presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian. The emphasis is placed on ideas...
Springer, 2024. — 322 p. Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence...
Kluwer Academic Publishers, 1991. — 336 p. This volume presents an authoritative, unified overview of the methods and results concerning the global properties of linear differential equations of order n (n>=2). It does not, however, seek to be comprehensive. Rather, it contains a selection of results which richly illustrate the unified approach presented. By making use of...
Springer, 2023. — 669 p. Defined as solutions of linear differential or difference equations with polynomial coefficients, D-finite functions play an important role in various areas of mathematics. This book is a comprehensive introduction to the theory of these functions with a special emphasis on computer algebra algorithms for computing with them: algorithms for detecting...
Basel: Birkhäuser, 2023. — 310 p. In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was...
Монография. — Новосибирск: Новосибирский государственный технический университет (НГТУ), 2022. — 481 с. Монография посвящена исследованию дифференциальных уравнений (ДУ), описывающих волновые процессы в неоднородных средах, свойств семейств кривых и поверхностей с помощью группового и геометрического анализа. Изучена группа эквивалентности уравнения эйконала и других ДУ и ее...
М.: Юнити-Дана, 2017. — 646 с. Книга объединяет круг вопросов, связанных с исследованием качественных свойств решений нелинейных обыкновенных дифференциальных уравнений, краевых задач для уравнений в частных производных и связанных с ними спектральных задач. Содержатся подробные доказательства результатов, полученных авторами как классическими, так и оригинальными методами...
De Gruyter, 2019. — 136 p. Introduction General context Operators with constant second-order term Equations in divergence form Extensions Bibliography Index
Berlin: de Gruyter, 2020. — 310 p. Acknowledgment Introduction Preliminary concepts Solvability of the abstract Cauchy problem Global in time continuation of solutions Definitions, properties, estimates, and inequalities Navier–Stokes equation in 2D and 3D N-D Navier–Stokes equation, an extended discussion Cauchy’s problem for 2-D quasi-geostrophic equation Dirichlet’s problem...
De Gruyter, 2002. — 220 p. Preface Auxiliary information from functional analysis and theory of differential equations The weak approximation method Identification problems for parabolic equations with Cauchy data The identification of the source function for a system of composite type and parabolic equation. The behavior of the problem’s solution under t —> + ∞ The problem of...
Пер. с англ. Т.Н. Рожковская. — Новосибирск: Тамара Рожковская, 2006. — 102 с. — (Белая серия в математике и физике). — ISBN 5901873211. Представлены некоторые методы исследования нелинейных уравнений с частными производными, объединенные идеей слабой сходимости приближенных решений и использующие структуру нелинейности для обоснования предельного перехода. Описаны методы,...
New York: Springer, 2014. — 238 p. This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of...
Перевод с англ. А.М. Зверкина, Г.А. Каменского. — Под ред. Л.Э. Эльсгольца. — М.: Иностранная литература, 1961. — 248 с. Книга посвящена дифференциально-разностным уравнениям, иначе называемыми уравнениями с отклоняющимся аргументом. Основное внимание уделяется линейным уравнениям с постоянными коэффициентами, - именно эти уравнения чаще всего встречаются в теории...
Berlin: de Gruyter, 2022. — 342 p. Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on...
World Scientific, 2023. — 326 p. This monograph is devoted to the existence and stability (Ulam–Hyers–Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are...
Boca Raton: CRC Press, 2024. — 313 p. Preface Editors Contributors Introduction Application of Differential Equation in a Flexible Production of Deteriorating Item under Trade Credit Policy Explosion in a Spherical Cavity Expanding with Decelerated Velocity Importance of Differential Equations in a Retailing Strategy under Credit Period Consideration Existence Results for the...
Учебное пособие. — М.: Московский государственный университет (МГУ) имени М.В. Ломоносова, 2020. — 96 с. Специальный курс для студентов физического факультета МГУ имени М.В. Ломоносова. Основные понятия Регулярные и сингулярные возмущения Асимптотическое приближение решения по параметру. Асимптотический ряд Формальная асимптотика Задача Коши для тихоновской системы Теорема...
Cham: Birkhäuser, 2023. — 768 p. This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that...
Berlin: de Gruyter, 2003. — 242 p. Inverse problems are an important and rapidly developing direction in mathematics,mathematical physics, differential equations, and various applied technologies (geophysics, optic, tomography, remote sensing, radar-location, etc.). In this monographdirect and inverse problems for partial differential equations are considered. The type of...
Basel: Birkhäuser, 2010. — 231 p. The goal of this book is to investigate the behavior of weak solutions of the elliptic transmission problem in a neighborhood of boundary singularities: angular and conic points or edges. This problem is discussed for both linear and quasilinear equations. A principal new feature of this book is the consideration of our estimates of weak...
Elsevier, 2006. — 539 p. Introduction Preliminaries Integral inequalities The laplace operator Strong solutions of the Dirichlet problem for linear equations The Dirichlet problem for elliptic linear divergent equations in a nonsmooth domain The Dirichlet problem for semilinear equations in a conical domain Strong solutions of the Dirichlet problem for nondivergence quasilinear...
Springer, 2021. — 142 p. This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in...
Berlin: Logos Verlag Berlin, 2015. — 336 p. This thesis is concerned with the numerical solution of boundary value problems (BVPs) governed by nonlinear elliptic partial differential equations (PDEs). To iteratively solve such BVPs, it is of primal importance to develop efficient schemes that guarantee convergence of the numerically approximated PDE solutions towards the exact...
Казань: Казанский университет, 2009. — 58 с. Данное пособие возникло на основе спецсеминаров со студентами, специализирующимися по кафедре дифференциальных уравнений, а также слушателями ФПК. Во второй части рассматриваются основные элементы теории обыкновенных дифференциальных уравнений в банаховых пространствах. Приведены доказательства многих сформулированных утверждений....
Казань: Казанский университет, 2009. — 84 с. Данное пособие возникло на основе спецсеминаров со студентами, специализирующимися по кафедре дифференциальных уравнений, а также слушателями ФПК. В первой части рассматриваются основные элементы дифференциального исчисления в банаховых пространствах. Приведены доказательства многих сформулированных утверждений. Пособие предназначено...