@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} }