Research topics

We study a class of nonlinear kinetic equations derived from a generalized Vlasov-Poisson model under certain physical assumptions. We prove the local existence and uniqueness of solutions in a framework of analytic functions using the Banach fixed-point theorem.
Vlasov equations, analytic solutions, analytic norms, fixed point method.

Effect of anisotropic diffusivity, development of gradients due to discontinuities in diffusivity.

Diffusion of multicomponent systems, cross diffusion systems, mathematical properties, renormalized solutions, uniqueness of weak solutions.

Thermodynamics, Soret effect, diffusion of binary liquid, heterogeneous diffusion equation.