The asymptotic analysis of boundary value problems in parameter-dependent domains is a rapidly developing field of research in the theory of partial differential equations, with important applications in electrostatics, elasticity, hydrodynamics and fracture mechanics. Building on the work of Ciarlet and Destuynder, this book provides a systematic coverage of these methods in multi-structures, i.e. domains which are dependent on a small parameter e in such a way that the limit region consists of subsets of different space dimensions. An undergraduate knowledge of partial differential equations and functional analysis is assumed.

Asymptotic Analysis of Fields in Multi-Structures (Oxford Mathematical Monographs)

Science & Math

Movchan, Alexander

Maz'ya, Vladimir

Kozlov, Vladimir

Mathematics

Oxford University Press

Applied Partial Differential Equations (Oxford Texts in Applied and Engineering Mathematics)

Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied PDEs contains many new sections and exercises Including, American options, transform methods, free surface flows, linear elasticity and complex characteristics.

Arts & Photography

Ockendon, John

Howison, Sam

Lacey, Andrew

Music

Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied P.D.Es contains many new sections and exercises Including, American options, transform methods, free surface flows, linear elasticity and complex characteristics.

History & Philosophy

Applied Partial Differential Equations

A vibrant field of study, partial differential equations arise in mathematical models whose dependent variables change continuously as functions of several independent variables (often space and time). Their power lies in their universality: there is a huge and ever-growing range of real-world problems to which they can be applied, from fluid mechanics and electromagnetism to probability and finance. This book is a lively and well-written guide to both the theory and applications of PDEs. It examines such questions as the well-posedness of a PDE problem and the conditions under which solutions change little with small changes in input. It also examines the problem of establishing the accuracy of a numerical solution to a PDE, an increasingly important question given the power of new numerical methods and software.

A vibrant field of study, partial differential equations arise in mathematical models whose dependent variables change continuously as functions of several independent variables (often space and time). Their power lies in their universality: there is a huge and ever-growing range of real-world problems to which they can be applied, from fluid mechanics and electromagnetism to probability and finance. This book is a lively and well-written guide to both the theory and applications of PDEs. It examines such questions as the well-posedness of a PDE problem and the conditions under which solutions change little with small changes in input. It also examines the problem of establishing the accuracy of a numerical solution to a PDE, an increasingly important question given the power of new numerical methods and software.

There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions. The main focus of the present text is on two topics: (a) asymptotics of Green’s kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables. This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations.

Green's Kernels and Meso-Scale Approximations in Perforated Domains (Lecture Notes in Mathematics, 2077)

Nieves, Michael

Springer

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Books by Movchan, Alexander

See the best price to sell, buy, or rent books by Movchan, Alexander. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Asymptotic Analysis of Fields in Multi-Structures (Oxford Mathematical Monographs)

Applied Partial Differential Equations (Oxford Texts in Applied and Engineering Mathematics)

Applied Partial Differential Equations (Oxford Texts in Applied and Engineering Mathematics)

Applied Partial Differential Equations

Applied Partial Differential Equations

Green's Kernels and Meso-Scale Approximations in Perforated Domains (Lecture Notes in Mathematics, 2077)