**Fall 2022. MATH5099. Section 007. **

### Methods in Partial Differential Equations (PDE III)

**Instructor:**
Luan Thach Hoang

Office: MA 208. Phone: (806) 834-3060.

Email address: *luan.hoang@ttu.edu*

Homepage:
*http://www.math.ttu.edu/~lhoang/*

Office hours: MW 2pm-3:30pm.

**Classroom:** CMLL 101 (Classical and Modern Languages and Literatures Bulding). **Time:** MWF 11 am - 11:50 am.

**Course website:**
*http://www.math.ttu.edu/~lhoang/2022Fall-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 5: Sobolev Spaces (Review)
- Chapter 6: Second Order Elliptic Equations
- Chapter 7: Linear Evolution Equations
- Chapter 8: Calculus of Variations
- Other topics in Elliptic, Parabolic and Hyperbolic Equations

**Homework:** Optional.

**Reading assignment:** One reading assignment at the end of the semester.