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 - <p>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.</p>