MATH6042 - Topics in Differential Equations II - 2018/19

Announcement

• Here is the references: [Download file]
• Assessment type: 10% for participation, 40% for oral presentation, and 50% for report on a research topic. The oral presentation and research topics will be arranged very soon.

General Information

Lecturer

• Prof. Renjun DUAN
  • Office: LSB 206
  • Tel: 39437977
  • Email:

Time and Venue

• Lecture: Th 2:30PM - 5:15PM Lady Shaw Bldg 222

Pre-class Notes

• A review of mathematical topics in collisional kinetic theory (Villani)
• Hypocoercivity (Villani)
• Diffusive limit of Vlasov-Poisson-Fokker-Planck system (Ghani and Masmoudi)
• Spatially homogenous theory (Chapter 6 of CIP)
• Application of Fourier transformation
• Boltzmann around vacuum
• Large-data existence theory by DiPerna-Lions
• Existence theory for Vlasov-Poisson (Chapter 4 of Glassey's book)
• Vlasov-Poisson around vacuum (Bardos and Degond)
• Initial understanding of Landau damping
• Uniqueness of Vlasov-Poisson system

Lecture Notes

• Topic on Fokker-Planck operator (Covers: Fokker-Planck operator; Dissipative structure; Regularity; Hydrodynamic limit)
• Topic on Boltzmann operator (Covers: Spatially homogenous problem; Application of Fourier transformation; Spatially inhomogeneous theory including the large-date theory, vacuum problem and perturbation theory)
• Topic on Vlasov-Poisson system (Covers: Solutions around vacuum; Dispersive property; Weak stability problem)

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