Analysis of models from the crystal growth theory and image processing. Looking for new approaches giving nice properties of solutions in order to have relations to computer simulations.
Free boundary problems, especially the dynamic contact angle problem. Existence, stability and asymptotic behavior.
Parabolic systems. Existence and regularity of solutions. Relation to non-Newtonian fluids.
Mathematical Biology. Studies of morphogen transport and chemotactic processes related to cancer growth simulations.
To develop numerical analysis for solving unstable differential problems which occur in many science and engineering applications and which can be classified as the inverse - or ill-posed ones. They are among the most complicated ones. Thermoviscoelasticity and Cahn-Hilliard equations. Qualitative theory and asymptotic analysis of solutions to equations of fluid mechanics, attractors.
