Project Grant 2606567

The National Science Foundation Division of Mathematical Sciences awarded the University of Maryland Baltimore County $150,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct collaborative research on the regularity, stability, and control of poroelastic filtration systems.

The award funds development of foundational mathematical theory for partial differential equations that model interactions between moving fluids and deformable porous materials. The project addresses gaps in the underlying mathematics by developing tools to assess the reliability of these models, characterize solution behavior in relation to the system's physics, and incorporate solution methods into frameworks for numerical computation and control theory. Work focuses on fluid-poroelastic structure interactions governed by coupled PDE systems, including free fluids, deformable porous media, multilayer interactions, and interface effects. Primary objectives include developing regularity theory and characterizing spectral properties for coupled dynamics across physically relevant regimes—inertial, quasi-static, compressible, incompressible cases, and physical geometries with boundary and interface effects. Results will provide the foundation for stability analyses, control strategies, and accurate numerical simulations applicable to geosciences, environmental engineering, energy extraction, and biomedical modeling.

Performance occurs in Baltimore, Maryland, with a period of performance from August 1, 2026, through July 31, 2029. This is a Project Grant assistance type.