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Topological Optimization and Optimal Transport

In the Applied Sciences

Ed. by Bergounioux, Maïtine / Oudet, Édouard / Rumpf, Martin / Carlier, Guillaume / Champion, Thierry / Santambrogio, Filippo

Series:Radon Series on Computational and Applied Mathematics 17

    139,95 € / $196.00 / £126.99*

    eBook (PDF)
    Publication Date:
    August 2017
    Copyright year:
    2017
    ISBN
    978-3-11-043041-7
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    Overview

    Aims and Scope

    By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered.

    Contents
    Part I

    • Geometric issues in PDE problems related to the infinity Laplace operator
    • Solution of free boundary problems in the presence of geometric uncertainties
    • Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies
    • High-order topological expansions for Helmholtz problems in 2D
    • On a new phase field model for the approximation of interfacial energies of multiphase systems
    • Optimization of eigenvalues and eigenmodes by using the adjoint method
    • Discrete varifolds and surface approximation

    Part II

    • Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem
    • Optimal transportation theory with repulsive costs
    • Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations
    • On the Lagrangian branched transport model and the equivalence with its Eulerian formulation
    • On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows
    • Pressureless Euler equations with maximal density constraint: a time-splitting scheme
    • Convergence of a fully discrete variational scheme for a thin-film equatio
    • Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

    Details

    xii, 420 pages
    105 Fig.
    Language:
    English
    Type of Publication:
    Monograph
    Keyword(s):
    Shape representations; shape optimization; relaxation theory; optimal transport

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    M. Bergounioux; É. Oudet; M. Rumpf; G. Carlier; T. Champion; F. Santambrogio.

    More by Bergounioux, Maïtine:

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