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.