Research Opportunity in Differential Equations

The Differential Equations Research Group of IMath invites graduate (MS or PhD) students to collaborate on a topic on homogenization of partial differential equations (PDEs).

The asymptotic analysis of PDEs in commutative groups is an active research area due to its significance in modeling physical phenomena such as elasticity or thermal propagation in composite materials. However, work on the periodic homogenization of PDEs in the noncommutative setting, such as the Heisenberg group, is still limited.

In this research project, the asymptotic behavior of an elliptic PDE with mixed Signorini and Dirichlet boundary conditions in the Heisenberg group will be studied. The main novelty of this problem is the treatment of a variational inequality with Heisenberg differential operators that may model free boundary value problems in materials science and physics.

For more inquiries, please email Dr. Jose Ernie Lope at jclope[at]up[dot]edu[dot]ph.