Kategoria BISAC: Mathematics >> Differential Equations - General

Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods and results in a new area of application of Lie groups to difference equations, difference meshes (lattices), and difference functionals, this book focuses on the preservation of complete symmetry of original differential...

Ce cours est une introduction a la modelisation mathematique et a l'analyse numerique pour la chimie moleculaire quantique, un champ peu connu des mathematiciens et pourtant riche en sujets d'investigation. Le point de vue choisi est celui du mathematicien applique. Le cours est construit de maniere auto-consistante. Seules des notions de base en analyse fonctionnelle sont requises pour l'aborder. Les outils mathematiques plus elabores sont introduits progressivement et les connaissances necessaires en physique et en theorie spectrale sont regroupees dans des annexes. On presente d'abord...

This book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators. The book includes classic calculus as a special case. It will be accessible to graduate students and of benefit to researchers in PDEs and mathematical physics.

This book presents a comprehensive study of boundary value problems for linear and semilinear second order elliptic equations with measure data, especially semilinear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role.

Impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, etc. The questions of existence and stability of solutions for different classes of initial values problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems and relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its...