Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations. (Journal of Partial Differential Equations, 2017)
This paper consider the Cauchy problemfor a class of 1Dgeneralized Boussinesq equations utt-uxx-uxxtt+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.
Keywords: Generalized Boussinesq equations; Cauchy problem; global existence; nonexistence