Differential calculus and equations

The book deals with the localization approach to the index problem for elliptic operators.

An asymmetric norm is a positive definite sublinear functional p on a real vector space X.

This book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space.

In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory.

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics.

Evolution equations of hyperbolic or more general p-evolution type form an active field of current research.

This book contains survey papers based on the lectures presented at the 3rd International Winter School "e;Modern Problems of Mathematics and Mechanics"e; held in January 2010 at the Belarusian State University, Minsk.

This volume contains surveys as well as research articles broadly centered on spectral analysis.

This book contains an expanded version of lectures delivered by the authors at the CRM in Spring of 2009.

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems.

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples.

Concentration analysis provides, in settings without a priori available compactness, a manageable structural description for the functional sequences intended to approximate solutions of partial differential equations.

This volume contains twenty-one solicited articles by speakers at the IWOTA 2009 workshop, ranging from expository surveys to original research papers, each carefully refereed.

The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators.

This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations, and liquid crystal system.

Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations.

Inequalities arise as an essential component in various mathematical areas.

This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval.

The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions.

This special volume focuses on optimization and control of processes governed by partial differential equations.

This textbook presents basic notions and techniques of Fourier analysis in discrete settings.

The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy.

Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces.

This book deals with the modeling, analysis and simulation of problems arising in the life sciences, and especially in biological processes.

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field.

This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009.

The book provides a quick overview of a wide range of active research areas in partial differential equations.

The volume originates from the 'Conference on Nonlinear Parabolic Problems' held in celebration of Herbert Amann's 70th birthday at the Banach Center in Bedlewo, Poland.

This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems.

The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the applications to aerodynamics.

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The purpose of the volume is to bring forward recent trends of research in hypercomplex analysis.

Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory.

This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs).

This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method.

This monograph examines the stability of various coupled systems with local Kelvin-Voigt damping.

This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas.

This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance.

This textbook offers an engaging account of the theory of ordinary differential equations intended for advanced undergraduate students of mathematics.

This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory.

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations.

This book gathers peer-reviewed contributions submitted to the 21st European Conference on Mathematics for Industry, ECMI 2021, which was virtually held online, hosted by the University of Wuppertal, Germany, from April 13th to April 15th, 2021.

This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces.

This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice.

This study guide is designed for students taking courses in differential equations.

Over the past few decades, numerical simulation has become instrumental in understanding the dynamics of seas, coastal regions and estuaries.