Year: 2018
Author: Gongwei Liu, Shuying Tian
Journal of Partial Differential Equations, Vol. 31 (2018), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v31.n3.3
Journal of Partial Differential Equations, Vol. 31 (2018), Iss. 3 : pp. 224–236
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Cauchy problem