Sharp decay estimates for hyperbolic balance laws (Q1025000)

The authors study the spreading of rarefaction waves in entropy solutions for strictly hyperbolic and genuinely nonlinear systems of balance laws \(\partial_t u+\partial_x f(u)+g(u)=0\) with one spatial variable. They introduce measures describing the strength of waves and derive sharp decay estimates for the positive parts of this measures (corresponding to rarefaction waves), in the case of solutions with small total variation. These estimates are derived by comparison with a solution of Burgers' equation with specially constructed impulsive source containing the interaction potential.