On L sub 1contraction for systems of conservation laws
Abstract
The Cauchy problem for a 2 x 2 system of conservation laws in one dimension is u sub t + (f(u)) sub x = 0, x epsilon R, t greater than 0 u(x,0) = u sub 0 where u = (u sub 1, u sub 2), f = (f1 (u), f sub (u)). Such systems of equations usually come from the application of the laws of conservation for physical quantities like mass, momentum and energy, and arise in problems of gas dynamics, elasticity, oil reservoir simulation and other areas of engineering. The questions of decay and continuous dependence with respect to the initial data are central issues in the study of the problem above. The result proved here rules out the use of certain functionals to study the decay of solutions and is relevant to the issue of L sub 1 continuity with respect to the data.
 Publication:

Technical Summary Report Wisconsin Univ
 Pub Date:
 February 1986
 Bibcode:
 1986wisc.reptQ....P
 Keywords:

 Cauchy Problem;
 Conservation Equations;
 Conservation Laws;
 Decay;
 Problem Solving;
 Elastic Properties;
 Gas Dynamics;
 Kinetic Energy;
 Mass;
 Nonlinear Systems;
 Simulation;
 Physics (General)