Shock waves in conservation laws and reaction-diffusion equations
Join the course group in Telegram: link
Classes:
- March - June 2023. Tuesday, 1pm - 3pm and Friday, 9am - 11am
- Room 866, Department of Mathematics, Edifício Leme, PUC-Rio
Material:
- All materials in one file
- My notes (mainly handwritten): introduction - what this course is about? (Lecture 1), notes on 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 ‘‘Hyberbolic conservation laws in continuum physics’’, PDF
- L.C. Evans ‘‘Partial differential equations’’, PDE
- A. Bressan ‘‘Hyperbolic Conservation Laws: An Illustrated Tutorial’’, PDF
- H. Holden, N.H. Risebro ‘‘Front tracking for hyperbolic conservation laws’’, PDF
- Video lectures on Youtube closely related to the course:
- Constantine Dafermos, course of 9 lectures at IMPA: Hyberbolic conservation laws
- Henri Berestycki, mini course of 4 lectures at IMPA: Reaction-diffusion propagation in non-homogenous media
Exercises:
Exam:
Yulia Petrova
Assistant Professor at PUC-Rio
My research interests include PDEs and their applications to probability theory, fluid dynamics and real-world applications.