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Research Overview
Research Overview
My work is in nonlinear partial differential equations, particularly in problems where geometric or physical effects play a central role. I am generally interested in PDEs that reflect real structural or geometric constraints, and much of my work falls into two areas: flow–structure interaction and the hyperbolic Monge–Ampère equation.
Fluid–Structure Interaction
Fluid–Structure Interaction
I study beam and plate models coupled with aerodynamic flows. These systems mix geometric nonlinearities with nonlocal fluid forces, creating stability and well-posedness questions that classical approaches do not fully resolve. My work uses semigroup and quasilinear methods to understand how the coupling across the interface affects the dynamics, including a recent framework for an inextensible cantilever interacting with compressible potential flow.
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Hyperbolic Monge–Ampère
Hyperbolic Monge–Ampère
I also work on the hyperbolic Monge–Ampère equation, motivated by rigidity phenomena in negatively curved surfaces. This equation is highly sensitive to characteristic geometry, so I use a hodograph transformation to recast the problem in a form where weak solutions and energy behavior can be analyzed more clearly. I also build numerical schemes aligned with this structure, which help visualize and test the analytical predictions.
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