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.