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Functional analysis, calculus of var...

Botelho, Fabio Silva,

Functional analysis, calculus of variations and numerical methods for models in physics and engineering /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Functional analysis, calculus of variations and numerical methods for models in physics and engineering /Fabio Silva Botelho, Adjunct Professor.
作者:	Botelho, Fabio Silva,
出版者:	Boca Raton, FL :CRC Press ;2021.
面頁冊數:	xi, 576 p. :ill. ;27 cm
附註:	"A science publishers book."
標題:	Calculus of variations.
ISBN:	9780367356743 :

Functional analysis, calculus of variations and numerical methods for models in physics and engineering /
Botelho, Fabio Silva,

Functional analysis, calculus of variations and numerical methods for models in physics and engineering /Fabio Silva Botelho, Adjunct Professor. - Boca Raton, FL :CRC Press ;2021. - xi, 576 p. :ill. ;27 cm

"A science publishers book."

Includes bibliographical references (p. [569]-572) and index.

Metric spaces -- Topological vector spaces -- Hilbert spaces -- The Hahn-Banach theorems and the weak topologies -- Topics on linear operators -- Spectral analysis, a general approach in normed spaces -- Basic results on measure and integration -- The Lebesgue measure in Rn -- Other topics in measure and integration -- Distributions -- The Lebesgue and Sobolev spaces -- Basic topics on the calculus of variations -- More topics on the calculus of variations -- Convex analysis and duality theory -- Constrained variational optimization -- On central fields in the calculus of variations -- Global existence results and duality for non-linear models of plates and shells -- A primal dual formulation and a multi-duality principle for a non-linear model of plates -- On duality principles for one and three-dimensional non-linear models in elasticity -- A primal dual variational formulation suitable for a large class of non-convex problems in optimization -- A duality principle and concerning computational method for a class of optimal design problems in elasticity -- Existence and duality principles for the Ginzburg-Landau system in superconductivity -- Existence of solution for an optimal control problem associated to the Ginzburg-Landau system in superconductivity -- Duality for a semi-linear model in micro-magnetism -- About numerical methods for ordinary and partial differential equations -- On the numerical solution of first order ordinary differential equation systems -- On the generalized method of lines and its proximal explicit and hyper-finite difference approaches -- On the generalized method of lines applied to the time-independent incompressible Navier-Stokes system -- A numerical method for an inverse optimization problem through the generalized method of lines -- A variational formulation for relativistic mechanics based on Riemannian geometry and its application to the quantum mechanics context.

"The book discusses the basic concepts of functional analysis, measure and integration theory, calculus of variations and duality aiming 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 by the author"--

ISBN: 9780367356743 :NT$5952

LCCN: 2020019412Subjects--Topical Terms:

191127
Calculus of variations.

LC Class. No.: QA320 / B748 2021

Dewey Class. No.: 530.15/5

Functional analysis, calculus of variations and numerical methods for models in physics and engineering /
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300 $a xi, 576 p. : $b ill. ; $c 27 cm
500 $a "A science publishers book."
504 $a Includes bibliographical references (p. [569]-572) and index.
505 0 $a Metric spaces -- Topological vector spaces -- Hilbert spaces -- The Hahn-Banach theorems and the weak topologies -- Topics on linear operators -- Spectral analysis, a general approach in normed spaces -- Basic results on measure and integration -- The Lebesgue measure in Rn -- Other topics in measure and integration -- Distributions -- The Lebesgue and Sobolev spaces -- Basic topics on the calculus of variations -- More topics on the calculus of variations -- Convex analysis and duality theory -- Constrained variational optimization -- On central fields in the calculus of variations -- Global existence results and duality for non-linear models of plates and shells -- A primal dual formulation and a multi-duality principle for a non-linear model of plates -- On duality principles for one and three-dimensional non-linear models in elasticity -- A primal dual variational formulation suitable for a large class of non-convex problems in optimization -- A duality principle and concerning computational method for a class of optimal design problems in elasticity -- Existence and duality principles for the Ginzburg-Landau system in superconductivity -- Existence of solution for an optimal control problem associated to the Ginzburg-Landau system in superconductivity -- Duality for a semi-linear model in micro-magnetism -- About numerical methods for ordinary and partial differential equations -- On the numerical solution of first order ordinary differential equation systems -- On the generalized method of lines and its proximal explicit and hyper-finite difference approaches -- On the generalized method of lines applied to the time-independent incompressible Navier-Stokes system -- A numerical method for an inverse optimization problem through the generalized method of lines -- A variational formulation for relativistic mechanics based on Riemannian geometry and its application to the quantum mechanics context.
520 $a "The book discusses the basic concepts of functional analysis, measure and integration theory, calculus of variations and duality aiming 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 by the author"-- $c Provided by publisher.
650 0 $a Calculus of variations. $3 191127
650 0 $a Duality theory (Mathematics) $3 243402
650 0 $a Engineering mathematics. $3 182072
650 0 $a Functional analysis. $3 200585
650 0 $a Mathematical models. $3 182479
650 0 $a Mathematical physics. $3 190854
650 0 $a Numerical analysis. $3 182073