Project Grant 2204722

This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $230,826 to Michigan State University for research on nonlocal reaction-diffusion equations and Wasserstein gradient flows from August 1, 2022 to July 31, 2025. The research focuses on qualitative properties of solutions to nonlocal reaction-diffusion equations arising in biology and ecology; development and convergence analysis of deterministic particle methods for partial differential equations with an emphasis on their adaptation to robotic swarming in collaboration with engineers; and theory of gradient flows on measure spaces. A main aim is to extend the gradient flow formulation to nonlocal partial differential equations and those not mass-preserving, such as reaction-diffusion equations. The project also involves developing, implementing, and studying numerical methods for both local and nonlocal equations, with outcomes expected to provide insights into mechanisms driving biological and physical phenomena with potential applications in medicine and engineering.