Applied Partial Differential Equations Research Group
Professor Athanasios Tzavaras leads the Applied PDE group, which stands for
Applied Partial Differential Equations
Research group areas of expertise and current scientific interests:
analysis of partial differential equations, mathematical modeling, and numerical methods
Our group is interested in mathematical modeling, analysis and the development of numerical methods for evolutionary partial differential equations in fluid and solid mechanics.
Subjects of current interest include:
- Relative entropy and the comparison of thermomechanical theories in non-equilibrium thermodynamics.
- Modeling and analysis of dilute suspensions: Passage from microscopic descriptions to the equations of viscoelasticity at the macroscopic scale.
- Formation of singularities in solid mechanics (cavitation, shear bands).
- Numerical methods for hyperbolic-parabolic systems.
- Propagation of oscillations in hyperbolic and dispersive media, homogenization.
