Kategoria BISAC: Mathematics >> Differential Equations - General

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.

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research...

The book offers a hollistic approach to the theory and numerics of random differential equations from an interdisciplinary and problem-centered point of view. In this interdisciplinary work, the authors examine state-of-the-art concepts of both dynamical systems and scientific computing.

The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science.

Contents:
Preface
Sobolev Space and Preliminaries
The Vanishing Viscosity Method of Some Nonlinear Evolution System
The...

This monograph is a valuable contribution to the highly topical and extremly productive field of regularisation methods for inverse and ill-posed problems. The author is an internationally outstanding and accepted mathematician in this field. In his book he offers a well-balanced mixture of basic and innovative aspects. He demonstrates new, differentiated viewpoints, and important examples for applications. The book demontrates the current developments in the field of regularization theory, such as multiparameter regularization and regularization in learning theory.

The book is...

This monograph is an introduction to the theory of ordinary differential equations with jump conditions at discrete moments of time.

From the contents:

• Pulse differential equations and inclusions
• Linear systems with multivalued trajectories
• Method of averaging in systems with pulse action
• Averaging of differential inclusions
• Differential equations with discontinuous right-hand side

Included in this set:

Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R

With the needed mathematical and computational tools, this book provides a solid foundation in formulating and solving real-world PDE problems in various fields from applied mathematics, engineering, and computer science to biology and medicine, includes supporting documentation and step-by-step guidance, and features R codes that can be easily and conveniently used by readers.

Topical coverage includes:...