This National Science Foundation project grant of $361,251 will support research at Louisiana State University from July 1, 2022 to June 30, 2025 under the Mathematical and Physical Sciences program (CFDA 47.049). The university will investigate novel numerical schemes for least squares problems involving elliptic partial differential equations that model steady state problems in science and engineering. This includes developing finite element methods for least squares problems in data fitting...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) in the amount of $209,999 supports research on the theoretical understanding of partial differential equations arising from physics and how kinetic models can elaborate on the shortcomings of original scientific theories. The research project, conducted by Louisiana State University, consists of four main components: 1) establishing the well-posedness and conditional...
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...
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 from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $382,648 to the University of Texas at Austin for research investigating partial differential equations methods in the study of interfaces from July 1, 2022 to June 30, 2025. The award supports research training for graduate students and postdoctoral researchers in two thematic areas: developing mesoscale and macroscopic models...
This $100,972 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on nonlinear partial differential equations and their applications in fields such as crystal growth, combustion, and game theory. The primary investigator (PI) will study the regularity, large-time behavior, and qualitative properties of solutions to these equations, which have connections to areas like the calculus of...
This National Science Foundation project grant of $428,169 supports research in harmonic analysis and partial differential equations at the University of Illinois from August 2022 through July 2025. The award is funded through the Mathematical and Physical Sciences program (CFDA 47.049). The project involves foundational research in harmonic analysis and analysis of partial differential equations with a focus on long-time dynamical properties and decay estimates. Specific areas of study...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in three canonical classes of nonlinear partial differential equations. The key objectives are to: Advance the understanding of existence, regularity, and large-time behavior of solutions for multi-dimensional Euler alignment equations, nonlinear conservation laws, and the pressure-less system. This involves developing novel...
This $399,583 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research to develop numerical algorithms that can estimate solutions to partial differential equations (PDEs) without full boundary condition information. The research aims to enable improved modeling and forecasting capabilities across various applications, including meteorology, biology, and engineering design. The primary awardee, Texas...