Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations.
Year: 2017
Author: Xiuyan Peng, Yi Niu
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 2 : pp. 95–110
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v30.n2.1
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 2 : pp. 95–110
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Generalized Boussinesq equations