Perturbation of a shock wave
The Cauchy problem is considered for the perturbed Hopf equation \(u_t+u\), \(u_x=\varepsilon f(u)\), \(\varepsilon\to 0\). The solution in the continuity domain can be expended in the standard asymptotic series in integral powers of the small parameter. An asymptotic representation is found for the line of propagation of the shock wave.
scientific article; zbMATH DE number 1465893