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A³N²M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models

Proceedings of the 50th John H. Barrett Memorial Lectures

  • Book
  • © 2023

Overview

Editors:
  1. Tadele Mengesha

    1. Department of Mathematics, University of Tennessee, Knoxville, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Abner J. Salgado

    1. Department of Mathematics, University of Tennessee, Knoxville, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Presents a thorough overview of latest developments in nonlocal modeling
  • Includes key contributions by experts in approximation, analysis, and applications of nonlocal models
  • Suitable for researchers and graduate students in integro-partial differential

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 165)

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About this book

This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.

Keywords

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Plenary Lectures

    1. Front Matter

      Pages 1-1
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    2. CTRW Approximations for Fractional Equations with Variable Order

      • V. N. Kolokoltsov
      Pages 3-25

    3. Fractional Elliptic Problems on Lipschitz Domains: Regularity and Approximation

      • Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
      Pages 27-99

    4. Regularity Estimates and Open Problems in Kinetic Equations

      • Luis Silvestre
      Pages 101-148

  3. Invited Contributions

    1. Front Matter

      Pages 149-149
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    2. An Optimization-Based Strategy for Peridynamic-FEM Coupling and for the Prescription of Nonlocal Boundary Conditions

      • Marta D’Elia, David J. Littlewood, Jeremy Trageser, Mauro Perego, Pavel B. Bochev
      Pages 151-174

    3. Nonlocal Diffusion Models with Consistent Local and Fractional Limits

      • Qiang Du, Xiaochuan Tian, Zhi Zhou
      Pages 175-213

    4. A One-Dimensional Symmetric-Force-Based Blending Method for Atomistic-to-Continuum Coupling

      • Elaine Gorom-Alexander, Xingjie Helen Li
      Pages 215-251

    5. A Note on Estimates of Level Sets and Their Role in Demonstrating Regularity of Solutions to Nonlocal Double-Phase Equations

      • Tadele Mengesha, James M. Scott
      Pages 253-293

    6. An Overview of Almost Minimizers of Bernoulli-Type Functionals

      • Mariana Smit Vega Garcia
      Pages 295-319

  4. Back Matter

    Pages 321-321
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Editors and Affiliations

  • Department of Mathematics, University of Tennessee, Knoxville, USA

    Tadele Mengesha, Abner J. Salgado

About the editors

Tadele Mengesha: Tadele Mengesha is a professor of mathematics at the University of Tennessee, Knoxville. He obtained his PhD in Mathematics in 2007 from Temple University. His main area of research is applied analysis with particular interest in regularity theory for solutions of partial differential and integral equations, asymptotic analysis, and calculus of variations.
Abner J. Salgado: Abner J. Salgado is a professor of mathematics at the University of Tennessee, Knoxville. He obtained his PhD in Mathematics in 2010 from Texas A&M University. His main area of research is the numerical analysis of nonlinear partial differential equations, and related questions.

Bibliographic Information

  • Book Title: A³N²M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models

  • Book Subtitle: Proceedings of the 50th John H. Barrett Memorial Lectures

  • Editors: Tadele Mengesha, Abner J. Salgado

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-3-031-34089-5

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-34088-8Published: 12 August 2023

  • Softcover ISBN: 978-3-031-34091-8Due: 12 September 2023

  • eBook ISBN: 978-3-031-34089-5Published: 11 August 2023

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: XIII, 321

  • Number of Illustrations: 4 b/w illustrations, 31 illustrations in colour

  • Topics: Numerical Analysis, Analysis, Mathematical Modeling and Industrial Mathematics

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