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Partial Differential Equations

Partial differential equations is a many-faceted subject.  Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations.  Examples are the vibrations of solids, the flow of fluids, the diffusion of chemicals, the spread of heat, the interactions of photons and electrons, the radiation of electromagnetic waves. Today, partial differential equations have developed into a vast subject that interacts with many other branches of mathematics, such as complex analysis, differential geometry, harmonic analysis, probability, mathematical physics, and mathematical finance and economics.

Activities

Regular Faculty

  • Matthew Gursky

    Professor

    Differential Geometry and Partial Differential Equations

  • Qing Han

    Notre Dame Collegiate Professor in the Department of Mathematics

    Differential Geometry and Partial Differential Equations

  • Alex Himonas

    Professor

    Partial Differential Equations

  • Yangyang Li

    Assistant Professor

    Differential Geometry, Partial Differential Equations, Geometric Measure Theory

  • Gerard Misiolek

    Professor

    Analysis and Geometry

  • Liviu Nicolaescu

    Professor, Director of Undergraduate Honors Math Program

    Topology and Probability

  • Matthew Novack

    Associate Professor

    Fluid mechanics and kinetic theory

  • Marianna Russkikh

    Assistant Professor

    Complex analysis, probability theory and mathematical physics

  • Jiahong Wu

    Professor

    Fluid Mechanics and Partial Differential Equations

Visiting and Postdoctoral Faculty

  • Bryan Dimler

    Rev. Howard J. Kenna, C.S.C. Research Fellow

    nonlinear PDE, geometric analysis, and geometric measure theory

Emeriti Faculty

Graduate Students

  • Zi Peng

    Real Analysis/PDE

  • Mingyu Yu

    Real Analysis/PDE