Mathematics of phase transition and thermomechanical models:

• Systems of phase-field and phase-relaxation. Stefan problems.
• Thermodynamical consistent phase change systems (e.g.: Penrose-Fife model, phase transitions driven by microforces).
• Integrodifferential evolution systems. Modeling of memory effects.
• Evolution models for metallic alloys. Allen-Cahn and Cahn-Hilliard equations.
• Approach to phase change systems via hysteresis operators.
• Elasticity, thermoelasticity. Modeling damage in elastic bodies.
• General doubly nonlinear equations or systems and their applications.

Infinite-dimensional dynamical systems:

• Long time behavior of evolution equations. Omega-limit sets.
• Dissipative dynamical systems. Global and exponential attractors.
• Regularity of attractors. Exponential attractors. Finite-dimensionality.
• Applications to nonlinear evolution systems especially related to physical models.

More general partial differential equations:

• Regularity of solutions to elliptic and parabolic boundary value problems.
• Existence and approximation theory for PDE's with nonlocal terms.