Time-periodic solutions to a class of quasilinear wave equations
The authors show the existence of a set of functions \(c=c(u)\) for which the quasilinear wave equation \(u_ t - v_ x\), \(v_ t - c^ 2(u)u_ x = 0\) possesses a spatially and temporally periodic solution. The function \(c\) satisfies \(c(-u) = c(u) \geq c_ 0 > 0\), \(c'(u)>0\) for \(u>0\), and \(c'\) has a jump at zero. The solution they construct is shock- free with the only singularities being centered simple waves.
scientific article; zbMATH DE number 399277
scientific article