Justification of nonlinear geometric optics for a system of conservation laws
Systems of conservation laws \(u_t+f(u)_x=0\) with the initial condition of the type \[ u_i(0,x)=\varepsilon h_i\left( x,{\psi_i (x)\over \varepsilon}\right) \] are considered in particular in one space dimension. The author proves propagation theorems and estimates, deals with the conditions on the phase \(\psi\) and gives global existence theorem with the asymptotic estimate.
scientific article; zbMATH DE number 1026540
scientific article