Differential calculus and equations

This book discusses recent trends and developments in the area of nonlinear evolution equations.

The equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc.

This book presents the topological derivative method through selected examples, using a direct approach based on calculus of variations combined with compound asymptotic analysis.

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation.

Finite volume methods are used for various applications in fluid dynamics, magnetohydrodynamics, structural analysis or nuclear physics.

This monograph considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow, and proves the existence of global regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux.

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, "e;Fractals and Related Fields II,"e; held in June 2011.

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Professor Ralph Kleinman was director of the Center for the Mathematics of Waves and held the UNIDEL Professorship of the University of Delaware.

The latest advancements in time scale calculus are the focus of this book.

Much progress has been made in recent years on the issue of asymptotic behavior of problems set in cylinders.

For introductory courses in Differential Equations.

This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology.

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete).

This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations.

A lively and engaging look at some of the ideas, techniques and elegant results of Fourier analysis, and their applications.

Asymptotic Analysis of Singular Perturbations

This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations.

The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems.

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators.

Beginning with the works of N.

The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications.

A collection of self contained state-of-the art surveys.

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.

This book explains the notion of Brakke's mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory.

A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.

This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations.

This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday.

This book gathers peer-reviewed, selected contributions from participants of the 6th International Workshop on Nonlinear and Modern Mathematical Physics (NMMP-2022), hosted virtually from June 17-19, 2022.

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 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.

Modern mathematics has become an essential part of today's physicist's arsenal and this book covers several relevant such topics.

This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods.

This book contains some contributions presented at the Applied Mathematics for Environmental Problems minisymposium during the International Congress on Industrial and Applied Mathematics (ICIAM) held July 15-19, 2019 in Valencia, Spain.

The techniques presented here are useful for solving mathematical contest problems in algebra and analysis.

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.

This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications.

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

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics.

The book is intended for all those who are interested in application problems related to dynamical systems.

Das Buch führt in die Theorie der Partiellen Differentialgleichungen ein, lediglich die Grundvorlesungen der Analysis werden vorausgesetzt.

This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations.