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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.
List of contents
CTRW approximations for fractional equations with variable order (Kolokoltsov).- Fractional Elliptic Problems on Lipschitz Domains: Regularity and Approximation (Borthagaray).- Regularity estimates and open problems in kinetic equations (Silvestre).- An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions (Littlewood).- Nonlocal diffusion models with consistent local and fractional limits (Du).- A one-dimensional symmetric force-based blending method for atomistic-to-continuum coupling (Li).- A note on estimates of level sets and their role in demonstrating regularity of solutions to nonlocal double phase equations (Mengesha).- An overview of Almost Minimizers of Bernoulli-Type Functionals (Garcia).
About the author
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.
