# Singular and Ill-Posed Problems for Partial Differential Equations in Continuum Mechanics

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · Pennsylvania State Univ University Park (PA) · $250,000

## Abstract

This project concerns the mathematical analysis and also the computation of certain phenomena in fluid mechanics and elasticity that are modeled using so-called partial differential equations. The aim of the project is both to advance a scientific understanding of important physical phenomena, as well as to make quantitative predictions whenever possible. The problems under study are motivated by real-life applications with potential societal benefits. In the first part of the project, the Principal Investigator studies the interaction between incompressible fluid flows and walls, focusing on two problems. The first problem pertains to the motion of inviscid fluids in containers with permeable walls that allow for injection and suction, and how the rate and direction of injection and suction affects the flow. This problem has many applications from the study of fluids in sections of pipelines, to modeling of underground wells. The second problem focuses on a simplified model of the Earth, consisting in a fluid-filled solid shell, representing the Earth’s crust and mantle, containing a solid core, and on the long-time combined motion of the fluid-solid system. In the second part of the project, the Principal Investigator examines the effects of material transport and diffusion in certain fluid models. Two problems are considered. The first problem concerns flame front propagation in combustion and phase separation in fluid mixtures, for instance binary alloys. The second probl

## Key facts

- **NSF award ID:** 2511023
- **Awardee organization:** Pennsylvania State Univ University Park (PA)
- **SAM.gov UEI:** NPM2J7MSCF61
- **PI:** Anna L Mazzucato
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $250,000
- **Funds obligated:** $250,000
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2027

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2511023

## Citation

> US National Science Foundation, Award 2511023, Singular and Ill-Posed Problems for Partial Differential Equations in Continuum Mechanics. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2511023. Licensed CC0.

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