Differential calculus and equations

These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form.

This volume contains lecture notes from the coursesgiven by Vlad Bally and Rama Cont at the Barcelona Summer School on StochasticAnalysis (July 2012).

This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view.

This book mostly results from a selection of papers presented during the 11th IFAC (International Federation of Automatic Control) Workshop on Time-Delay Systems, which took place in Grenoble, France, February 4 - 6, 2013.

This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties.

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation.

The heart of the book is the development of a short-time asymptotic expansion for the heat kernel.

In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis.

This book offers a thoroughand self-contained exposition of the mathematics of time-domain boundaryintegral equations associated to the wave equation, including applications toscattering of acoustic and elastic waves.

This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples.

This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic.

This text provides the first comprehensive treatment of the discrete fractional calculus.

This book highlights the current state of Lyapunov-type inequalities through a detailed analysis.

Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces.

This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A.

These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering.

This monograph presents an introduction to some geometric and analytic aspects of the maximum principle.

This works focuses on regularity theory for solutions to the p-Laplace equation in the Heisenberg group.

The book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium.

This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations.

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems.

This book is devoted to background material and recently developed mathematical methods in the study of infinite-dimensional dissipative systems.

This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics.

This book may be used as reference for graduate students interested in fuzzy differential equations and researchers working in fuzzy sets and systems, dynamical systems, uncertainty analysis, and applications of uncertain dynamical systems.

This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs).

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations.

The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations.

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics.

This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type.

This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes.

The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "e;Conference on Hamiltonian Systems and Celestial Mechanics 2014"e; (HAMSYS2014) (15 abstracts) and at the "e;Workshop on Virus Dynamics and Evolution"e; (12 abstracts), both held at the Centre de Recerca Matematica (CRM) in Barcelona from June 2nd to 6th, 2014, and from June 23th to 27th, 2014, respectively.

This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations.

This three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation.

In these notes we consider two kinds of nonlinear evolution problems of von Karman type on Euclidean spaces of arbitrary even dimension.

This monograph presents results of the analytical and numerical modeling of convective heat and mass transfer in different rotating flows caused by (i) system rotation, (ii) swirl flows due to swirl generators, and (iii) surface curvature in turns and bends.

The lessons in this fundamental text equip students with the theory of Computer Assisted Design (CAD), Computer Assisted Engineering (CAE), the essentials of Rapid Prototyping, as well as practical skills needed to apply this understanding in real world design and manufacturing settings.

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations.

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations.

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2013.

This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations.

This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas.

This book is intended for students of computational systems biology with only a limited background in mathematics.

This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently.

This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday.

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area.

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain.

Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering.

This book explains many fundamental ideas on the theory of distributions.

Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms.

This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.