On the asymptotic formula for the solution of nonlocal boundary value perturbation problems for hyperbolic equations

In the present paper we consider the nonlocal boundary value perturbation problem { ?2?2u(t,x)?t2-(a(x)ux(t,x))x+du(t,x)=f(t,x),0<t<T,x?(0,l),u(0,x)=au(T,x)+f(x),x?[0,l],u'(0,x)=ßu'(T,x)+?(x),x?[0,l],u(t,0)=u(t,l),ux(t,0)=ux(t,l),0=t=T for hyperbolic equation with an arbitrary ? ? (0, 8) parameter multiplying the derivative term. An asymptotic formula for the solution of this problem with a small ? parameter is presented. © 2021 Author(s).