My research focuses on the modeling, mathematical analysis, and numerical simulation of multispecies systems - systems in which several interacting species or components influence each other’s behavior. I study diffusion processes where the movement of one species depends on the others, a phenomenon captured by cross-diffusion models. These models arise in contexts ranging from biology and ecology to gas mixtures and medical applications.

In classical diffusion, species move along their own concentration gradients, and the process can be described by a set of conservation laws with fluxes satisfying Fick’s second law of diffusion. In contrast, in cross-diffusion systems, the flux of one species depends not only on its own concentration gradient but also on the gradients of all other species. Classical diffusion can be represented by a diagonal, positive definite matrix. Cross-diffusion models, however, involve a non-diagonal, often non-symmetric, and possibly non-positive definite matrix. The resulting equations are strongly coupled and typically nonlinear.

My work addresses the analytical and numerical challenges posed by these nonlinear systems of conservation laws, when diffusion can also be anisotropic. I am interested in deriving macroscopic models from kinetic descriptions and developing robust numerical schemes that preserve the structural properties of the underlying equations. Applications of my research include ion transport (Poisson–Nernst–Planck-type models), aerosol dynamics, and diffusion processes in materials science, such as the formation of solar panels (Physical Vapor Deposition model). Recently, I have also started exploring the coupling of cross-diffusion systems through a moving interface.

In particular, I have experience with entropy methods and finite volume schemes.