Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations.

Abstract

This paper consider the Cauchy problemfor a class of 1Dgeneralized Boussinesq equations u_tt-u_xx-u_xxtt+u_xxxx+u_xxxxtt= f(u)_xx. By utilizing the potential well method and giving some conditions on f(u), we obtain the invariance of some sets and obtain the threshold result of global existence and nonexistence of solutions.