Trustees of Boston University was awarded a three-year $300,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) to conduct research on dynamic bifurcation of patterns through spatio-temporal heterogeneity. The university will investigate how naturally occurring and man-made spatial patterns interact with heterogeneities in time and space using mathematical models from physics and other scientific domains. Researchers will...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research aimed at advancing the mathematical analysis of nonlinear partial differential equations. The research has three main focus areas: (1) studying fluid dynamics problems with free boundaries, such as water waves, tsunamis, and hurricanes; (2) investigating the dynamics of gases and plasmas under physical kinetic boundary conditions,...
This Project Grant award of $300,000.00 from the National Science Foundation's (NSF) Division of Mathematical Sciences supports research to develop new mathematical methods and techniques for analyzing multi-dimensional partial differential equations (PDEs) that govern fluid flows and related phenomena. The research project, titled "Analysis of Hyperbolic and Mixed-Type PDEs in Conservation Laws and Applications," aims to advance the mathematical understanding of multi-dimensional...
The National Science Foundation (NSF) awarded a $299,998 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to Georgia Tech Research Corporation to conduct fundamental research on the dynamics of nonlinear partial differential equation (PDE) systems that model fluid flow and nonlinear waves. The research will focus on analyzing the local dynamics near steady states in incompressible fluid PDEs with free surfaces, as well as a class of nonlinear...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program is supporting research by The Trustees of Columbia University in the City of New York to advance the theoretical understanding of partial differential equations, free boundary problems, and related mathematical concepts. The $273,927 award, with a performance period from July 1, 2024 to June 30, 2027, focuses on developing new methods and regularity theories for specific...
This Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) supports research focused on addressing fundamental questions in partial differential equations and optimization theory. The $291,367 award, spanning July 2024 to June 2027, will advance the Principal Investigator's work on characterizing extremal functions for Morrey's inequality, studying solutions to the pressureless Euler system, and...
This five-year, $209,505 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support research at Montana State University on elliptic and parabolic partial differential equations. The principal investigator will advance understanding of how solutions behave for more complex PDEs that model quantum behavior, systems with microscopic structure, and time-dependent phenomena. One component involves using properties of harmonic...
The National Science Foundation awarded The Johns Hopkins University a $320,648 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will support research into various aspects of the theory of partial differential equations as they relate to the dichotomy between regularity and singularity formation. The Principal Investigator will pursue research in regularity theory and geometric properties for partial differential equations arising in the theory of...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $400,000 Project Grant to Duke University on August 1, 2023 under the Mathematical and Physical Sciences program (CFDA 47.049) to support innovative numerical methods for solving high-dimensional partial differential equations (PDEs). The key objectives of the 3-year project are to: (1) design and analyze neural-network parametrization for high-dimensional functions with symmetry constraints, and (2) develop and...
This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $292,823 in funding from August 1, 2022 to July 31, 2025 under the Mathematical and Physical Sciences program (CFDA 47.049). The award supports research and training at the University of Chicago on nonlinear partial differential equations with stochastic dependence, homogenization in random media, well-posedness in singular domains, mean-field games, and convergence of growth models. Key areas of...