Could some one please tell me wht is meant by L1 and L2 stability? concerning hyperbolic problems.. thank you

Hyperbolic system of equations such as Euler equations admit discontinuous solutions. Derivatives of discontinuous functions exist only in generalized (distributional) sense. Since L2 norm involves derivatives of function, L1 norm is used in the stability considerations for hyperbolic systems of conservation laws. L2 norm is used for elliptic and parabolic systems.

L1 and L2 stability simply measure the growth of instabilities in the solution, hence the notion of L1 and L2 stability.

could u please tell me what an L1 and L2 norm is? i am just a beginner..

I did a Google search and found this: http://mathworld.wolfram.com/L2-Norm.html

Hi I could n ot able to understand what does that mean by "Derivatives of discontinuous functions exist only in generalized (distributional) sense."

and L2 norm of what has the derivatives ....