The National Science Foundation awarded a $179,538 Project Grant to The Ohio State University under the Mathematical and Physical Sciences program (CFDA 47.049) to support research analyzing initial and boundary value problems for dispersive and diffusive partial differential equations. The award period is from October 1, 2022 through June 30, 2024. The University will use Uniform Transform Method techniques to extend previous results on unbounded domains to bounded intervals in very low and...
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's Mathematical and Physical Sciences program (CFDA 47.049) provides $232,812 to The Johns Hopkins University from July 1, 2022 to June 30, 2025 to improve understanding of dispersive partial differential equations. Key products include research on the long-time behavior of solutions to critical scaling equations like the Schrödinger maps problem and focusing/mass-critical nonlinear Schrödinger equation. Additional work will analyze energy...
This Project Grant award of $302,028.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) supports fundamental research on nonlinear hyperbolic and dispersive partial differential equations (PDEs). The award aims to deepen the understanding of these PDEs, which are critical for describing natural phenomena across scales, by investigating long-term dynamics, singularity formation, and the stability of special solutions. Key...
The National Science Foundation awarded North Carolina State University a three-year, $368,594 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to develop new mathematical and computational tools for nonlinear hyperbolic systems of partial differential equations. The university will use the funding to design efficient high-order numerical methods for conservation and balance laws that go beyond consistency, stability, and convergence. Key activities include...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will provide $150,000 to the University of Wisconsin System to conduct research on asymptotic behavior in partial differential equations from various scientific applications. The key focus areas include: (1) studying long-time propagation and front structure in reaction-diffusion equations in heterogeneous environments; (2) analyzing long-time and white-noise limits of...
This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) Project Grant award of $169,408, starting on June 1, 2024 and ending on August 31, 2026, supports research at the University of North Carolina at Chapel Hill (UNC-CH) on nonlinear stochastic partial differential equations and their applications. The project aims to develop a mathematical understanding of these equations, which arise in complex dynamic phenomena like global economic shifts and turbulent...
The National Science Foundation (NSF) awarded a $310,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to The Washington University's Office of Sponsored Research Services Division. The grant supports fundamental mathematical research at the intersection of analytic function theory, harmonic analysis, and operator theory. The proposed work aims to leverage "testing theorems" to address open questions in these areas, which have applications in...
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...
The National Science Foundation awarded a $279,707 Project Grant to the University of Washington under the Mathematical and Physical Sciences program (CFDA 47.049). The grant funds research on the regularity theory of measures and dispersive partial differential equations over a five-year period concluding June 30, 2027. The Mathematical and Physical Sciences program supports fundamental research and education in mathematics and the physical sciences to promote scientific progress and strengthen...