I am an applied mathematician interested in applied/numerical analysis of partial differential equations (PDEs). My PhD research focused on PDEs posed on evolving surfaces — in particular the Cahn-Hilliard equation (and variants thereof):
Recently I have been interested in free/moving boundary problems, for example the system governing the motion of a rigid body immersed in a viscous fluid:
and fully nonlinear PDEs, such as systems arising from the theory of mean field games:
C. M. Elliott and T. Sales, "A constructive approach to a fluid-rigid body interaction problem", 2025. (In preparation).
T.Sales and I. Smears, "Fully nonlinear second-order mean field games with nondifferentiable Hamiltonians", 2025. (arXiv)
C. M. Elliott and T. Sales, "An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential", 2026. (To appear in IMA Journal of Numerical Analysis) (arXiv)
C. M. Elliott and T. Sales, "The evolving surface Cahn-Hilliard equation with a degenerate mobility", 2026. (Nonlinear Analysis: Real World Applications) (arXiv)
C. M. Elliott and T. Sales, "A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential", 2025. (Numerische Mathematik) (arXiv)
C. M. Elliott and T. Sales, "Navier-Stokes-Cahn-Hilliard equations on an evolving surface", 2025. (Interfaces and Free Boundaries) (arXiv)
T. Sales, "A (tangential) Navier-Stokes-Cahn-Hilliard system on an evolving surface", 2024. In Oberwolfach Report 21, (3) "Interfaces, Free Boundaries, and Geometric Partial Differential Equations".