Bøger i Differential and Integral Equations and Their Applications serien

Presents a survey of methods and results in an application area of Lie groups to difference equations and difference meshes (lattices). This work focuses on the formulation and mathematical substantiation of exact symmetry preservation in difference models, such as difference equations and meshes.

Focuses on the analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. This book provides estimates of the operator norms for various ranges of the wave number variation, and then examines the spectral properties of these operators.

Starting from an elementary level and finishing with the most recent results, this book gives a systematic exposition of both analytical and topological aspects of elliptic theory on manifolds with singularities. The presentation includes a review of the main techniques of the theory of elliptic equations, offers a comparative analysis of various approaches to differential equations on manifolds with singularities, and devotes considerable attention to applications of the theory. A glossary, numerous illustrations, and many examples help readers master the subject. Clear exposition, up-to-date coverage, and accessibility lay the groundwork for continuing studies and further advances in the field.

Gives a systematic exposition of both analytical and topological aspects of elliptic theory on manifolds with singularities. This work includes a review of the techniques of the theory of elliptic equations, offers an analysis of approaches to differential equations on manifolds with singularities, and focuses on applications of the theory.

This volume presents a systematic mathematically rigorous exposition of methods for studying linear partial differential equations on the basis of quantization of the corresponding objects (states, observables and canonical transformations) in the phase space.

A reference source for researchers, engineers and students of applied mathematics, mechanics, control theory and the engineering sciences, this title contains about 3000 first order partial differential equations with solutions.