This federal Project Grant award, provided by the National Science Foundation's Engineering program (CFDA 47.041), supports the development of a unified polynomial optimization framework to analyze and control nonlinear partial differential equations (PDEs). The $397,375 grant, awarded to Arizona State University, aims to create computational methods and algorithms that enable the solution, analysis, and control of nonlinear PDEs, making these techniques more accessible to researchers and engineers without extensive mathematical expertise. The key focus of this 3-year collaborative project between US and UK investigators is to parameterize positive polynomial Lyapunov functions in a distributed space using positive partial integral operators, allowing for the efficient computational verification of stability properties of nonlinear PDEs. The resulting algorithms will be applied to problems of fluid flow with transition to turbulence, as well as data-based models of magnetohydrodynamic plasma in tokamak nuclear fusion reactors. The project seeks to develop user-friendly software to automate the process, facilitating the rapid prototyping of complex data-based models across a broad class of nonlinear PDEs.
Mod # | Description | Reason For Modification | Federal Obligation (Click to sort descending) | Date (Click to sort ascending) |
|---|---|---|---|---|
| Not listed | $397.4k | 5/30/25 |