Partial Differential Equations

Research Advisors for Partial Differential Equations

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John Burns , bio
Professor Burns' current research is focused on computational methods for modeling, control, estimation and optimization of complex systems where spatially distributed information is essential. This includes systems modeled by partial and delay differential equations. Recent applications include modeling and control of thermal fluids, design and thermal management systems and optimization of mobile sensor networks.
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Guher Camliyurt , bio
Dr. Camliyurt's research interests include mathematical fluid dynamics, nonlinear waves, and unique continuation problems for general elliptic and parabolic PDEs.
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Honghu Liu , bio
Professor Liu's research focuses on the design of effective low-dimensional reduced models for nonlinear deterministic and stochastic PDEs as well as DDEs. Applications to classical and geophysical fluid dynamics are actively pursued. Particular problems that are addressed include bifurcation analysis, phase transition, surrogate systems for optimal control, and stochastic closures for turbulence.
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Eyvindur Ari Palsson , bio
Associate Professor Palsson conducts research in harmonic analysis, geometric measure theory, combinatorics, number theory and partial differential equations.
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Shu-Ming Sun , bio
Professor Sun's research interests include the mathematical theory of fluid mechanics, the theory of partial differential equations, and applied nonlinear analysis.

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Fangchi Yan , bio
Dr. Yan studies partial differential equations (PDEs) that are motivated from the modeling of physical phenomena and real-world problems in general. His research focuses on the problem of well-posedness for nonlinear dispersive equations, including the Korteweg-de Vries (KdV) equation and the nonlinear Schrödinger (NLS) equation.
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John Taylor Burleson , bio
Instructor Burleson is currently engaged with teaching with an interest in computational fluid dynamics.
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Keoni Castellano , bio
Dr. Castellano is a Postdoctoral Associate who conducts research on the mathematical analysis of infectious disease models.
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Xin Yang , bio
I am an instructor whose main research area is Partial Differential Equations.