**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.

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