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Volume 31, Issue 3
Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem

Gongwei Liu & Shuying Tian

DOI: 10.4208/jpde.v31.n3.3

J. Part. Diff. Eq., 31 (2018), pp. 224-236.

Published online: 2018-09

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  • Abstract

The Cauchy problem for a viscoelastic equation with nonlinear damping and source terms is considered. We establish the nonexistence result of global solutions with initial energy controlled above by a critical value by modifying the method introduced in a work by Autuori et al. in 2010. Then we establish global existence for arbitrary initial data or the energy in potential well. These improve earlier results in the literatures.

  • Keywords

Cauchy problem viscoelastic equation global existence blow up.

  • AMS Subject Headings

35B44, 35L05, 35R09, 45K05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gongweiliu@126.com (Gongwei Liu)

sytian@whut.edu.cn (Shuying Tian)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-224, author = {Liu , Gongwei and Tian , Shuying}, title = {Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {3}, pages = {224--236}, abstract = {

The Cauchy problem for a viscoelastic equation with nonlinear damping and source terms is considered. We establish the nonexistence result of global solutions with initial energy controlled above by a critical value by modifying the method introduced in a work by Autuori et al. in 2010. Then we establish global existence for arbitrary initial data or the energy in potential well. These improve earlier results in the literatures.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n3.3}, url = {http://global-sci.org/intro/article_detail/jpde/12706.html} }
TY - JOUR T1 - Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem AU - Liu , Gongwei AU - Tian , Shuying JO - Journal of Partial Differential Equations VL - 3 SP - 224 EP - 236 PY - 2018 DA - 2018/09 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n3.3 UR - https://global-sci.org/intro/article_detail/jpde/12706.html KW - Cauchy problem KW - viscoelastic equation KW - global existence KW - blow up. AB -

The Cauchy problem for a viscoelastic equation with nonlinear damping and source terms is considered. We establish the nonexistence result of global solutions with initial energy controlled above by a critical value by modifying the method introduced in a work by Autuori et al. in 2010. Then we establish global existence for arbitrary initial data or the energy in potential well. These improve earlier results in the literatures.

Liu , Gongwei and Tian , Shuying. (2018). Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem. Journal of Partial Differential Equations. 31 (3). 224-236. doi:10.4208/jpde.v31.n3.3
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