Max Gunzburger (Florida State University), Applied Mathematics Colloquium

Tea will be at 3:30 in 330 Phillips Hall

Title: Integral equation modeling for nonlocal diffusion and mechanics

Abstract: We consider the use of integral equations as nonlocal models for diffusion. An important example are fractional Laplacian equations although our theory and numerics apply to problems that cannot be modeled by fractional derivative models. We discuss theories for the analysis and numerical analysis of the models considered, relying on a nonlocal vector calculus to define weak formulations in function space settings. We also briefly discuss the nonlocal, continuum peridynamics model for solid mechanics. [Based on joint works with Marta D’Elia, Qiang Du, Richard Lehoucq, Xiaochuan Tian, and F. Xu.]