Asymptotic behavior of global classical solutions to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small BV data
First, the author recall John's formula on the decomposition of waves with some supplements. Then some estimations are obtained which are used in the proof of main Theorem 1.1. The results of the main Theorem 1.1 can be applied to many physical models, like the mixed initial boundary value problem for the quasilinear hyperbolic system of the planar motion of an elastic string. In the author opinion, of particular interest is the system of the motion of the relativistic string in the Minkowski space-time, as an application of main Theorem 1.1, the asymptotic behavior of the classical solutions of the mixed initial boundary value problem with small data for this system. Based on the existence result on the global classical solution, it is proved that when time tends to infinity, the solution approaches a combination of regular traveling wave solutions, provided that that the corresponding norm of the initial and boundary data is bounded and the BV norm of the initial and boundary data is sufficiently small.
scientific article; zbMATH DE number 5675043
scientific article