Shock Waves in Conservation Laws and Reaction–Diffusion Equations
Graduate course (MSc) · PUC-Rio, March–June 2023 · Tuesdays 1–3pm and Fridays 9–11am, room 866, Edifício Leme
Lecture notes
All materials in one file (PDF)
My notes (mainly handwritten): introduction — what this course is about (Lecture 1); notes on the wave equation (Lectures 2–4); notes on conservation laws (Lectures 5–14); notes on reaction–diffusion equations (Lectures 15–24).
Books
J. Smoller, Shock Waves and Reaction–Diffusion Equations (PDF) · C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics (PDF) · L. C. Evans, Partial Differential Equations (PDF) · A. Bressan, Hyperbolic Conservation Laws: An Illustrated Tutorial (PDF) · H. Holden, N. H. Risebro, Front Tracking for Hyperbolic Conservation Laws (PDF)
Video lectures closely related to the course
Constantine Dafermos, nine lectures at IMPA: Hyperbolic conservation laws · Henri Berestycki, mini-course of four lectures at IMPA: Reaction–diffusion propagation in non-homogeneous media
Exercises and exam
Problem-solving sessions: Session 1 · Session 2 · Session 3 · Session 4
Homework: List 1 · List 2 · List 3 · List 4 · List 5
Exam: Questions (PDF)