Lectures: MWF 2:00-2:50 a.m. in APM 5829
Instructor: Kate Okikiolu
email: okikiolu@math.ucsd.edu
Office Hours: Wednesday or Thursday by appointment.
Text
: Partial Differential Equations by
Lawrence C. Evans, Graduate Studies
in Mathematics 19, American Mathematical Society
231B Syllabus:Chapters 7 and 3 and further topics:
Second order evolution equations, non-linear first order equations,
further topics.
Grading:
Homework
and/or Class Presentations
This is a continuation from 231A and 231B.
| wk | date | Monday | Wednesday | Friday |
| 1 | 4/3 | Second order parabolic equations | Weak Solutions | Weak Solutions |
| 2 | 4/10 | Galerkin approximation | Galerkin approximation | Problem session |
| 3 | 4/17 | Regularity | Regularity | Regularity |
| 4 | 4/24 | Regularity | Higer Reguality | Harnack Principle |
| 5 | 5/1 | Hyperbolic Equations | Existence | Uniqueness |
| 6 | 5/8 | finite propogation | regularity | higher regularity |
| 7 | 5/15 | hyperbolic systems | hyperbolic systems | hyperbolic systems |
| 8 | 5/22 | semigroups | semigroups | semigroups |
| 9 | 5/29 | Holiday | characteristics | characteristics |
| 10 | 6/5 | Hamilton-Jacobi equations | Hamilton-Jacobi equations | Lagrangian |
Math Department Syllabus for 231A-B-C: Existence and uniqueness theorems. Cauchy-Kowalewski theorem, first order systems. Hamilton- Jacobi theory, initial value problems for hyperbolic and parabolic systems, boundary value problems for elliptic systems. Green's function, eigenvalue problems, perturbation theory.