Reaction-diffusion Equations
نویسنده
چکیده
I have recently worked in the area of partial differential equations (PDE), specifically reaction-diffusion equations, drift-diffusion equations, and fluid dynamics. These equations model physical processes such as combustion, mixing, or turbulence, and my main interest has been in long term dynamics of their solutions as well as in the formation of singularities. I consider myself an applied analyst and use in my work techniques from PDE and other areas, including spectral theory and stochastic processes. In the past I also worked on the spectral theory of Schrödinger operators, orthogonal polynomials, and graph theory, but I will only focus on some of my recent PDE results here and single out ten of them.
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