Instructor: Irene M. Gamba
Class hours: T-TH 2:00-3:30 pm, by Zoom Address to be announced
Additional Meeting Hour when needed: TBA
Website: http://www.ma.utexas.edu/users/gamba/teaching.html
Office: RLM 10.166 -- Phone: 471-7150
Office Hours: by appointment
Email: gamba@math.utexas.edu
· Recommended Text: Partial Differential Equations by L.C. Evans, Graduate Studies in Mathematics 19, AMS. Second Edition
· Additional notes to be distributed on Canvas
· For a review: Elementary Applied Partial Differential Equations, by Richard Haberman.
Syllabus:
Brief description: This is the first semester of a year long course which serves as an Introduction to the theory of linear and nonlinear partial differential equations. Part of the class will be devoted to the issues of the existence and other properties (deep regularity, stability, etc.) for linear equations (elliptic, parabolic, hyperbolic and dispersive), discussing Green’s functions and methods involving local and non-local functional analysis and the interplay in between the two approaches through variational formulation and methods of super and sub-solutions to solve the linear boundary value problem in general domains.
In addition, the course will include introductory issues to the theory of the solutions some important non-linear equations like entropy solutions for hyperbolic conservation laws, viscosity solutions for Hamilton-Jacobi equations, and some topics on nonlinear second order PDEs.
Class requisites: There will be suggested problems. At end of semester, students will make 20 to 30 minutes presentation of related papers.
There will be no final exam.
Prerequisite: Some basic knowledge of real analysis and undergraduate ODEs and PDEs, as well as different issues discussed in the classical graduate Applied Mathematics Methods Prelim course, is strongly recommended.
Individuals not registered for this course and wish to audit
the class, please contact I.M. Gamba by e-mail for permission and to get access
to Canvas. This is important in order to
be able to connect to the zoom class meetings.