Applications of the asymptotic method to the investigation of a hyperbolic impulsive system
The author constructs an asymptotic approximation for the periodic solutions of the hyperbolic equation \[ u_{tt}-c^ 2u_{xx}+\lambda^ 2u=\epsilon f(u,u_ t,u_ x) \] with impulse input in the time \(t_ 0\) given by \[ u_ t(t_ 0+0,x)-u_ t(t_ 0- 0,x)=\epsilon I(u_ t(t_ 0-0,x)). \] Here \(\epsilon\) is a small parameter and f and I are sufficiently smooth functions.
scientific article; zbMATH DE number 4115147