Volume 30, Issue 2
Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations.

Xiuyan Peng & Yi Niu

J. Part. Diff. Eq., 30 (2017), pp. 95-110.

Published online: 2017-05

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  • 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.

  • Keywords

Generalized Boussinesq equations Cauchy problem global existence nonexistence

  • AMS Subject Headings

35L75, 35B44, 35A01

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yanyee_ny07@126.com (Xiuyan Peng)

349773509@qq.com (Yi Niu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-30-95, author = {Peng , Xiuyan and Niu , Yi }, title = {Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations.}, journal = {Journal of Partial Differential Equations}, year = {2017}, volume = {30}, number = {2}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v30.n2.1}, url = {http://global-sci.org/intro/article_detail/jpde/10001.html} }
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 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.
Xiuyan Peng & Yi Niu. (2019). Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations.. Journal of Partial Differential Equations. 30 (2). 95-110. doi:10.4208/jpde.v30.n2.1
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