Andrej Zlatoš

Professor Zlatoš works in the areas of applied analysis and partial differential equations (PDEs), where his interest is primarily in parabolic and elliptic PDEs and fluid dynamics. His recent work has been focused on reaction-diffusion and advection-diffusion equations. These model evolution of quantities such as densities of chemicals or animal species, or temperatures of combusting media, which are subject to diffusion in an environment as well as a reactive process (chemical reaction, birth and death, combustion) and/or transport by a flow.

There are a lot of interesting questions about these equations, particularly about long-term behavior of their solutions. Do they spread or become extinct, and what are the factors that affect the answer? If the former, what is the speed of this spreading? If the latter, how quickly does extinction happen? How do the solutions look like in general and does this correspond to our expectations based on the original physical/chemical/biological processes? Questions of existence and regularity of solutions to these and related equations also sometimes naturally arise from such studies. Answering all these questions often requires a combination of techniques from different areas of mathematics, including classical and functional analysis, PDEs, as well as the theory of probability and stochastic processes.

Zlatoš
Andrej
Caltech
2003
Associate Professor
Research Interests: 
Reaction-diffusion equations, Fluid dynamics, Spectral theory of Schrödinger operators, and Orthogonal polynomials
email: 
zlatos at math dot wisc dot edu
person_type: 
Faculty
web_site: 
http://math.wisc.edu/~zlatos