Spring 2013. MATH5342. Section 003.

Advanced Topics in Analysis I: Methods in Partial Differential Equations (PDE III)

Instructor: Luan Thach Hoang
Office: MA 208. Phone: (806) 742-2580 Ext 232. Fax: (806) 742-1112
Email address: luan.hoang@ttu.edu
Homepage: http://www.math.ttu.edu/~lhoang/
Office hours: TBA

Classroom: TBA. Time: TR 4:30 pm - 5:50 pm.

Course website: http://www.math.ttu.edu/~lhoang/2013Spr-M5099/

Text: Partial Differential Equations, 2nd edition, by Lawrence C. Evans, published by American Mathematical Society.
I will also make use of books by Gilbarg-Trudinger, Ladyzhenskaya-Solonnikov-Uraltseva, DiBenedetto, and Krylov.

Course Description: Developing theory for partial differential equations (PDE), particularly for the non-linear ones.

• Second-order elliptic, parabolic and hyperbolic equations: Weak solutions, Existence, Regularity.
• Various techniques are used to analyze these equations and properties of their solutions.

Course Outline:

• Chapter 7: Linear Evolution Equations
• Chapter 8: Calculus of Variations
• Chapter 9: Nonvariational Techniques
• Other topics in Elliptic, Parabolic and Hyperbolic Equations