TY - JOUR
T1 - Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations.
AU - Peng , Xiuyan
AU - Niu , Yi
JO - Journal of Partial Differential Equations
VL - 2
SP - 95
EP - 110
PY - 2017
DA - 2017/05
SN - 30
DO - http://doi.org/10.4208/jpde.v30.n2.1
UR - https://global-sci.org/intro/article_detail/jpde/10001.html
KW - Generalized Boussinesq equations
KW - Cauchy problem
KW - global existence
KW - nonexistence
AB -  This paper consider the Cauchy problemfor a class of 1Dgeneralized Boussinesq equations u<sub>tt</sub>-u<sub>xx</sub>-u<sub>xxtt</sub>+u<sub>xxxx</sub>+u<sub>xxxxtt</sub>= f(u)<sub>xx</sub>. 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.