Research Interests

My primary research is in partial differential equations (PDE). Many of the problems I deal with are called free boundary problems: One wants to solve a PDE in a domain, subject to boundary condition, while the boundary of this domain is not known in advance. Such situations arise in phase transition, tumor growth, film growth in semiconductor processing, propagation of cracks in elastic media, contact problems in elasticity, etc. I am also interested in finding properties of solutions to PDE, which are nonlinear and degenerate, and, in particular, in the blow-up of solutions of parabolic equations with nonlinear forcing terms. Another aspect of my work deals with homogenization: This situation arises when there are large oscillation in the medium, where one seeks to solve differential equations. Other areas of research include stochastic differential equations and control theory.

Membership Type


Election Year


Primary Section

Section 32: Applied Mathematical Sciences

Secondary Section

Section 11: Mathematics