Global existence and asymptotic behavior of classical solutions of quasilinear hyperbolic systems with linearly degenerate characteristic fields (Q876873)

The authors study the global existence and the asymptotic behavior of classical solutions of the Cauchy problem for quasilinear hyperbolic system \(\partial_t u +A(u)\partial_x u=0\) under the assumption that it is hyperbolic with constant multiple characteristic fields. They prove that the global \(C^1\)-solution exists uniquely if the BV-norm of the initial datum is sufficiently small. Moreover, when time \(t\) tends to infinity, this solution approaches a combination of \(C^1\)-traveling wave solutions.