Differential calculus and equations

This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations.

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields.

The book presents recent results and new trends in the theory of fluid mechanics.

This book is devoted to the study of positive solutions to indefinite problems.

These are the proceedings of the 24th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Svalbard, Norway in February 2017.

This book summarizes, defines, and contextualizes multiphysics with an emphasis on porous materials.

This book covers two essential PDE-based image processing fields: image denoising and image inpainting.

This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions.

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.

This book provides a systematic survey of classical and recent results on hyperbolic cross approximation.

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.

Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic.

This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators.

The second 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 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.

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 monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain.

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

This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes-parabolic and hyperbolic.

This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject.

This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes - non-orientable objects with a stratified structure.

The contributions in this volume give an insight into current research activities in Shape Optimization, Homogenization and Optimal Control performed in Africa, Germany and internationally.

Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.

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

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

Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians.

This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity.

This monograph presents  the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations.

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces.

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.

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations.

This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof.

This textbook provides a broad introduction to continuous and discrete dynamical systems.

This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16-20, 2015.

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field.

This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields.

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences.

This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.

This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE).

This book gathers papers from the International Conference on Differential & Difference Equations and Applications 2017 (ICDDEA 2017), held in Lisbon, Portugal on June 5-9, 2017.

This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry.

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

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

This book develops the foundations of "e;summability calculus"e;, which is a comprehensive theory of fractional finite sums.

This updated, second edition provides readers with an expanded treatment of the FEM as well as new information on recent trends in rapid prototyping technology.

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlomilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions.

This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference 'Stochastic Partial Differential Equations and Related Fields' hosted by the Faculty of Mathematics at Bielefeld University, October 10-14, 2016.

This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains.

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory.

This book presents and discusses the state of the art and future perspectives in mathematical modeling and homogenization techniques with the focus on addressing key physiological issues in the context of multiphase healthy and malignant biological materials.