Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering

The book discusses functional analysis, measure and integration theory, calculus of variations and duality, and their applications to variational problems of non-convex nature. It also covers numerical methods for these problems and recent research on Riemannian geometry applied to Quantum Mechanics and Relativity.

Format: Hardback
Length: 576 pages
Publication date: 03 November 2020
Publisher: Taylor & Francis Ltd

The book delves into the fundamental principles of functional analysis, measure and integration theory, calculus of variations, and duality, with a focus on their applications to variational problems of non-convex nature. These problems encompass a wide range of topics, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism, and more. To address these challenges, numerical methods have been developed using the generalized method of lines, including matrix finite dimensional approximations. These methods have proven invaluable in modeling and solving complex problems in flight mechanics and the Navier-Stokes system in fluid mechanics.

Furthermore, the book concludes with a comprehensive review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. This interdisciplinary approach sheds light on the connections between classical and quantum physics, offering insights into the fundamental nature of spacetime and matter.

The book is designed to cater to applied mathematicians and graduate students in applied mathematics. It provides a solid foundation in mathematical techniques and theories that are essential for understanding and solving complex problems in various fields. Physicists, engineers, and researchers in related fields will also find the book valuable as it offers a mathematical background applicable to their respective professional areas.

In summary, the book is a comprehensive resource that covers a wide range of topics in functional analysis, measure and integration theory, calculus of variations, and duality, with a particular emphasis on their applications to non-convex variational problems. It is an essential read for anyone interested in advancing their knowledge in applied mathematics and physics.

Weight: 1242g
Dimension: 185 x 260 x 41 (mm)
ISBN-13: 9780367356743