Fabio Silva Botelho, "Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering"
English | ISBN: 0367510030, 0367356740 | 2022 | 588 pages | PDF | 5 MB
The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity.
