**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