Gradient Flows

Author : Luigi Ambrosio
Publisher : Springer Science & Business Media
ISBN 13 : 376438722X
Total Pages : 334 pages
Book Rating : 4.28/5 ( download)

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Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

Author : Luigi Ambrosio
Publisher : Springer Science & Business Media
ISBN 13 : 3764373091
Total Pages : 330 pages
Book Rating : 4.92/5 ( download)

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Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.

Author : Anthony Bloch
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871362
Total Pages : 172 pages
Book Rating : 4.66/5 ( download)

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Download or read book Hamiltonian and Gradient Flows, Algorithms, and Control written by Anthony Bloch and published by American Mathematical Soc.. This book was released on with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of a conference held at the Fields Insitute and designed to bring together traditionally disparate fields of mathematical research. On such key interraction occurs between dynamical systems and algorithms. This volume explores many such interractions as well as related work in optimal control and partial differential equations.

Author : Karl-Theodor Sturm
Publisher : American Mathematical Society
ISBN 13 : 1470466961
Total Pages : 124 pages
Book Rating : 4.61/5 ( download)

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Download or read book The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces written by Karl-Theodor Sturm and published by American Mathematical Society. This book was released on 2023-11-27 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Author : Katz Gabriel
Publisher : World Scientific
ISBN 13 : 9814719684
Total Pages : 516 pages
Book Rating : 4.81/5 ( download)

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Download or read book Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary written by Katz Gabriel and published by World Scientific. This book was released on 2019-08-21 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it.The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters.

Author : Alessio Figalli
Publisher : European Mathematical Society
ISBN 13 : 3985470502
Total Pages : 0 pages
Book Rating : 4.01/5 ( download)

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Download or read book An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows written by Alessio Figalli and published by European Mathematical Society. This book was released on 2023-05-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text.

Author : Ben Andrews
Publisher : Springer Science & Business Media
ISBN 13 : 3642162851
Total Pages : 306 pages
Book Rating : 4.55/5 ( download)

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Download or read book The Ricci Flow in Riemannian Geometry written by Ben Andrews and published by Springer Science & Business Media. This book was released on 2011 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.

Author : Luigi Ambrosio
Publisher : Springer Nature
ISBN 13 : 3030721620
Total Pages : 250 pages
Book Rating : 4.26/5 ( download)

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Download or read book Lectures on Optimal Transport written by Luigi Ambrosio and published by Springer Nature. This book was released on 2021-07-22 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.

Author : Julianne M. Conley
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.81/5 ( download)

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Download or read book Modification of the MML Turbulence Model for Adverse Pressure Gradient Flows written by Julianne M. Conley and published by . This book was released on 1994 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Michael Hintermüller
Publisher : Springer Nature
ISBN 13 : 3030331164
Total Pages : 396 pages
Book Rating : 4.60/5 ( download)

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Download or read book Topics in Applied Analysis and Optimisation written by Michael Hintermüller and published by Springer Nature. This book was released on 2019-11-27 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.