Lessons in Nonlocal Modeling: Nonlocal Calculus, Operators, Properties, and Convergence

Dr. Petronela Radu

Abstract: The emergence of nonlocal theories as promising models in different areas of science (continuum mechanics, biology, and image processing) has led the mathematical community to conduct varied investigations of systems of integro-differential equations. In this talk, I will present some results we obtained for systems of integral equations with weakly singular kernels, flux-type boundary conditions, as well as some recent results on nonlocal Helmholtz-Hodge type decompositions with applications at both, theoretical, and applied levels.

Speaker’s Bio: Petronela Radu is the Leland J. and Dorothy H. Olson Professor in the Department of Mathematics at the University of Nebraska-Lincoln (UNL), where she also currently serves as the Undergraduate Chair.  Her research interests encompass a variety of areas in applied mathematics and mathematical analysis, in particular, in nonlinear partial and integro-differential equations, developing methods to study the behavior of nonlinear systems in mathematical physics. Her work has been supported by several agencies including the National Science Foundation (for research, as well as educational projects), Department of Energy, the Simons Foundation, and the Fulbright Foundation. She has published her research in high-quality peer-reviewed journals and received numerous invitations to speak at national and international meetings. Dr. Radu has been actively preparing a new generation of scientists by advising many undergraduates, graduates students, and postdoctoral fellows. She has received several awards for her innovative course Math in the City that exposes students to multidisciplinary research in collaboration with local businesses and research centers. Her teaching efforts have been recognized with a McClymont Award, as well as a College Teaching Award from the College of Arts and Sciences at UNL. Professor Radu is a member of the American Mathematical Society, the Society for Industrial and Applied Mathematics, the American Association for the Advancement of Science, the Association for Women in Science, the Association for Women in Mathematics, and the Mathematical Association of America.

Last Updated: February 11, 2022 - 10:42 am