MA8103 Non-Linear Hyperbolic Conservation Laws
General information
Background: In the course we study a class of nonlinear partial differential equation called hyperbolic conservation laws. These equations are fundamental in our understanding of continuum mechanical systems, and can be used to describe mass, momentum and enery conservation in mechanical systems. Examples of the use of conservation laws you may have seen in TMA4305 Partial differential equations and TMA4195 Mathematical modeling as well as in courses in physics and fluid mechanics. The equations share many properties that make numerical computations difficult. The equations may, for instance, develop singularities in finite time from smooth initial data. These equations have been extensively studied due to their importance in applications. Examples of applications include weather forecasting, flow of oil in a petroleum reservoir, waves breaking at a shore, and in gas dynamics.
Lecturers: Harald Hanche-Olsen and Helge Holden
Textbook: H. Holden and N. H. Risebro: Front Tracking for Hyperbolic Conservation Laws, Springer, Second edition 2015. The book exists as an eBook, and NTNU students can read and download it free of charge. There will be an inexpensive paperback edition called "MyCopy" that sells for EUR 24.95 (incl. shipping).
Time and place
For regular weeks the lectures are
Weekday | Time | Room |
---|---|---|
Monday | 08:15-10 | 734, Sentralbygg 2 |
Tuesday | 16:15-18 | 734, Sentralbygg 2 |
The lectures will be in English, and there will be an oral exam at the end of the semester. The first lecture will be Mon, Jan 15.
Lecture plan
Week | Day | Date | Material covered |
---|---|---|---|
3 | Mon | Jan. 15 | p. –9. |
Tue | Jan. 16 | p. 10–15 (very briefly), p. 53–56 (approx) | |
4 | Mon | Jan. 22 | p. 56– |
Tue | Jan. 23 | ? |