The Asymptotic Solution of the Initial Boundary Value Problem to a Generalized Boussinesq Equation

Abstract

The $L^2$ space solution of an initial boundary problem for a generalizeddamped Boussinesq equation is constructed. Certain assumptions on the coefficients ofthe equation are found to show the existence and uniqueness of the global solution to theinitial boundary problem. The explicit expression for the large time asymptotic solution isobtained.