Giulio Schimperna's scientific interests
Mathematics of phase transition and thermomechanical
- 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.
Last updated on
July, 21, 2008.