Differential calculus and equations

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Bedlewo, Poland in September 2015.

The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018.

This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987.

Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain.

This monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth's interior.

Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors' work on structurally stable planar quadratic polynomial differential systems.

This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch.

This book presents a series of challenging mathematical problems which arise in the modeling of Non-Newtonian fluid dynamics.

Sparse grids are a popular tool for the numerical treatment of high-dimensional problems.

This Brief reports on heat transfer from a solid boundary in a saturated porous medium.

The first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016.

The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research.

This volume presents the peer-reviewed proceedings of the international conference Imaging, Vision and Learning Based on Optimization and PDEs (IVLOPDE), held in Bergen, Norway, in August/September 2016.

This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation.

This book is devoted to computing the index of elliptic PDEs on non-compact Riemannian manifolds in the presence of local singularities and zeros, as well as polynomial growth at infinity.

Gott sprach: „Es werde Licht, und es ward .

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini.

Wave phenomena are ubiquitous in nature.

This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincare and Darboux to basic tools of modern mathematics.

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation.

This book aims to face particles in flows from many different, but essentially interconnected sides and points of view.

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems.

This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time.

Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems.

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications.

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "e;Intensive Research Program on Advances in Nonsmooth Dynamics 2016"e;, held at the Centre de Recerca Matematica (CRM) in Barcelona from February 1st to April 29th, 2016.

Presenting some recent results on the construction and the moments of Levy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction.

This book collects the abstracts of  the mini-courses and lectures given during the Intensive Research Program "e;Spaces of Analytic Functions: Approximation, Interpolation, Sampling"e; which was held at the Centre de Recerca Matematica (Barcelona) in October-December, 2019.

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior.

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22-25, 2016 in San Antonio, Texas.

This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics.

This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics.

New applications, research, and fundamental theories in nonlinear analysis are presented in this book.

This book collects chapters dealing with some of the theoretical aspects needed to properly discuss the dynamics of complex engineering systems.

This book focuses on the qualitative theory in structural mechanics, an area that remains underdeveloped.

This book contains advances on the theory and applications of time-delay systems with particular focus on interconnected systems.

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied.

This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses.

This volume comprises high-quality works in pure and applied mathematics from the mathematical communities in Spain and Brazil.

This volume presents lectures given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics.

This book discusses the numerical treatment of delay differential equations and their applications in bioscience.

This self-contained textbook discusses all major topics in functional analysis.

Stochastic Differential Equations and Diffusion Processes

In the study of Magnetic Positioning Equations, it is possible to calculate and create analytical expressions for the intensity of magnetic fields when the coordinates x, y and z are known; identifying the inverse expressions is more difficult.

This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering.

The main goal of this book is to provide an overview of the state of the art in the mathematical modeling of complex fluids, with particular emphasis on its thermodynamical aspects.

The Proceedings volume contains 16 contributions to the IMPA conference "e;New Trends in Parameter Identification for Mathematical Models"e;, Rio de Janeiro, Oct 30 - Nov 3, 2017, integrating the "e;Chemnitz Symposium on Inverse Problems on Tour"e;.

Functional analysis is an important branch of mathematical analysis which deals with the transformations of functions and their algebraic and topological properties.

Dedicated to Tosio Kato's 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics.