Asymptotics for a Class of a Semi-Linear Hyperbolic Equations with an Applicationto a Problem with Quadratic Nonlinearity

摘要

An initial boundary value problem for a semilinear hyperbolic equation isconsidered. An asymptotic theory for a class of problems is presented. This theory implies the well-posedness (in the classical sense) of the problem as well as the asymptotic validity of formal approximations on timescales. As an application of the theory initial boundary value problems are considered. These types of problems may serve as simple models for the vibrations of a taut string embedded in a nonlinear elastic medium.