L-1 stability for systems of conservation laws with a nonresonant moving source

In this paper, we study L-1 stability for systems of conservation laws with a moving source u(t) + f (u)(x) = g (x - ct, u). The source is assumed to be nonresonant in that its speed c is different from the characteristic spe eds of the system. We show that weak solutions are globally L-1 stable. Bas ed on the modi ed Glimm scheme, we construct a robust nonlinear functional H (t) = H [u (., t), v(., t)] which is equivalent to the L-1 distance of tw o solutions u, v and is nonincreasing in time t. This functional H [u, v] c onsists of a linear part L [u, v] measuring the L-1 distance, a quadratic p art Q(d) [u, v] measuring nonlinear couplings between waves of different ch aracteristic fields, a generalized entropy functional E[u, v] capturing the nonlinearity of characteristic fields, and a new functional Q(so) [u, v] m easuring the source effect on the L-1 distance.