Projected characteristics of conservation laws
The so called "characteristics" of a partial differential equations (PDE) are curves in the -plane along which the solution of the PDE is constant. In the special case of a conservation law (demonstrated here) the characteristics are straight lines.
- Increase the time and see if characteristics cross. Decrease number of characteristics to get a clearer look.
- Explain using the definition of the characteristics: What happens to at the point of intersection?
- Enter a new initial profile : How does the slope of affect the characteristics?
- Change the flow function : Try different convex (e.g. ) and concave (e.g. ) functions and observe the behavior of the characteristics.