Instructor: Dacian Daescu
Office: Neuberger Hall 313
Phone: (503) 725-3581
E-mail: daescu@pdx.edu
Office Hours: TR 12:30- 13:30
URL: http://web.pdx.edu/~daescu/

Class time and location: TR 14:00-15:15, Science Research & Teaching Center, 139B

Lecture Notes

• Weeks 1-2
  • Compact operators, weak convergence, Sobolev compact embeddings, Poincare-type inequalities, applications
  
  
• Weeks 2-3
  • Spectral Theory of Elliptic Operators
  
  
• Weeks 4-5
  • Spectral Theory of Elliptic Operators (continued). Hilbert-Schmidt Theorem
  • Minimization Principle. Ritz-Galerkin framework to approximate solution.
  
  
• Weeks 6-7
  • Optimization approach to spectral analysis
  • Linear Evolution Equations: Parabolic PDEs
  
  
• Weeks 7-8
  • Linear Evolution Equations: Hille-Yosida Theorem
  
  
• Week 9
  • Contraction Semigroups and Hille-Yosida Theorem
  • Maximum principles for elliptic problems
  
  
• Week 10
  • Harmonic functions, mean value property, strong maximum principle. Maximum principles for parabolic problems.

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  Homework assignments

  HW#1, due on January 26	HW#2, due on February 18	HW#3, due on March 8

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