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

摘要

This paper consider the Cauchy problem for a class of 1D generalized Boussinesq equations utt-u xx-u xxtt +uxxxx +uxxxxtt =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.