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

Gongwei Liu & Shuying Tian

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)

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@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} }
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